Code P0171, High fuel trims across all engine speeds, poor acceleration?

Hello, a couple things come to mind, with the very high mileage I would do a fuel injector balance test and see if they are all flowing the same. But I suspect a cat issue more than an injector issue. Although I would test for both, doing a back pressure test a the from A/F sensor location would tell you if there's a restricted exhaust. If the back pressure is over 2psi, which if that's the issue in this case it will be much higher. With such a small engine, the cat doesn't need to completely melted down to cause issues. Since you have already pretty much checked everything except the injector flow and the cat. Being that I believe the cat is part of the exhaust manifold on these, testing back pressure at the front A/F (02) sensor is the only real way to verify a restricted exhaust, I believe there is a 2nd cat half way down the exhaust as well that does not have an 02 behind it if I remember correctly, I'll check that in service info for you.

https://www.2carpros.com/articles/how-to-test-a-catalytic-converter

https://www.2carpros.com/articles/how-to-test-a-fuel-injector

Okay, it looks like this isn't the model with the cat being part of the exhaust manifold, which must be a different year I was thinking of.

Interestingly though, there is a valve adjustment for this engine, it's the more difficult method of measuring and adding different size shims. But you could take the valve cover off and look for any worn cam lobes, after checking the back pressure and injectors. You might just be dealing with clogged injectors or a bad tank of gas, with everything you have already done, you're only left with a couple possibilities now. Harbor Freight sells a vacuum gauge that also measures positive pressure up to 10psi, that's what I use with an old 02 sensor bored out as an adapter to measure back pressure at the front 02 location. Just don't leave the gauge on there more than a few seconds to measure back pressure or it will melt the gauge. Hook it up, have someone else start the engine, check it at idle, and then have them try to rev it a couple of times while you monitor the gauge. Then shut the engine off. You'll know right away if there is excessive back pressure.

I wasn't saying what you're experiencing is a result of worn cam lobes, which was just because of the very high mileage it has. The symptoms do fit a restricted exhaust, but if this issue has been on going since the cat was replaced, then that's not going to be the problem, I do wonder though what the condition of the previous cat was like. Did it come out in pieces, such as happens when one melts down and breaks apart? I have seen a broken cat come out but chunks of it get stuck in the rest of the exhaust, and if not checked would still be a restricted exhaust even with a new cat on there.

Just looking back over your list of repairs so far, you had listed the AF sensor as reading 1.23, is that milliamps?
And what is the reading of the rear 02 sensor at idle, and at 2000rpm if you can get it to go that high?
Since you have good scan data, some other things to check would the MAF reading at idle, on a small engine like this, it should be roughly around 1.3-2.3 grams per second or so (that is right from service info), (2.3g/s) at idle and 5.4-7.9 @ 2500rpm, on larger engines as a rule of thumb it will be about the same as the liters of the engine, so on a 5.0Liter it should be about 5g/s at idle.
And another test to run is a VE Test, here is a link to a good VE calculator.

https://atgtraining.com/atg-volumetric-efficiency-calculator/

This is a screenshot of the page, when you input your live data PIDs, it will calculate the EST_VE which is the Volumetric Efficiency of the engine, basically how well the engine is breathing, taking in air and allowing exhaust out. If you have a bad cat, or a MAF that is misreporting air flow the VE percentage will be low. You want the number to be as close to 100% as possible, it won't be, but for example the 94% is really good. The Instructions go through a bit more about the test. It's a helpful test to have in general,

But I agree with your diagnosis and thought process so far, the only thing that looks out of place is your AF sensor reading, on a Toyota it should be reading about 3.0 volts on an engine that's running at the correct air/fuel ratio, so that's why I asked about your reading there. If it's in milliamps or if that's the sensors voltage reading.
If it is reading 1.23volts at idle, that's way out of spec. I'm going to post the flow chart for you of the AF sensor's service info., I'm wondering if the parts store gave you either the incorrect part number or possibly a regular narrow band 02 sensor. Service info here is stating that anything under 3.0volts will cause high injection volumes (ill post all this for you). 25%+ which is what you are seeing.
And I know that Toyota's a really good at detecting oxygen sensor heater circuit issues, I've been down that road before. And you're not getting any heater circuit codes. So let me get this flow chart together for you, and you can go through it page by page and check your scan tool data.

Okay, so some of these scan tool data PIDs will depend on if you are using a Generic basic OBD2 scan tool in which the AF sensor voltage will be converted into a lower reading such as 0.62volts to 0.7volts. If you are using a scan tool and are on the Toyota manufacturers side reading live engine data you should see about 3.0volts on the B1S1 A/F sensor, so either way, something does not look right if that reading is in voltage.
I'm not going to post all of this since you have already checked a lot of it, but these first diagrams are for checking the manufacturers side of the scan tool, so selecting 2007 Toyota Corolla 1.8l etc. It gives a voltage reading of 3.0volts as being 14.7/1 ratio (normal). Page 4 shows that service info. I'll post the basic OBD2 data next.

This is the generic OBD2 scan tool flow chart for P0171, and it pretty much ends in "Replace the A/F sensor", and then "Replace the ECM". So, the only differences are the Output voltage readings. But this gives the same MAF readings. I haven't seen a Toyota AF sensor voltage drop that low on the manufacturers side of a scan tool, such as on an Autel or Topdon. Service info states the ECM converts the current flow into a voltage reading for live data, but I suppose that could vary depending on scan tools as well.

Yes,you're correct, if it was an air leak (vacuum leak) it would cause the fuel trims to come down towards zero at WOT, along with being in open loop, manifold vacuum would be closer to atmospheric pressure and the leak wouldn't effect fuel trims like they are, so yes it appears to be an actual lean condition. Your MAF readings suggest it's okay. They were a little better on the first pull, but still within spec. The AF ratio of 1.0 is stoichiometric (14.7/1) so 1.23 is an actual lean condition reading as well, you might be looking at clogged up, restricted injectors here.

You've really gone through almost everything, if an injector balance test shows different flow rates between the 4 of them, then you'll know there's at least an issue there. Really they should all flow exactly the same, have you done an injector balance test with a fuel gauge on the rail before? Where you get fuel pressure up to its max, then pulse each injector one at a time and watch for how much the fuel pressure drops on each injector. It requires an injector pulse tool or your Autel might be able to do it under special functions. You just need to re-prime the fuel pump each time, and once you run through all 4 injectors start the car to get the fuel out of all the cylinders, then you can re-run it again if needed. But if you find the fuel pressure drop is even a few psi off from other injectors, you know there's an issue there as well.

I think the ECM is at its complete limit for compensation, it just can't go any more than that percentage, it's a substituted value but extremely high, I think service info stated a 35% (or +25%) was the limit on positive fuel trims.

You could also graph the rear oxygen sensor voltage, and it should go full rich (high voltage) at a WOT run, and then it should have an injector cutoff when decel, my guess is you are going to see the rear 02 go lean instead. The MAF readings should be lower if this was a restricted exhaust, because the engine would not be able to take in more air if it can't let exhaust out.
As for the ECM being the problem, I would definitely rule out the injectors and back pressure first, making a call on an module is always a last resort and a difficult call as well. Because if a new ECM makes no difference you're back to square one. I'm surprised it's not setting other codes.

Whats your injector on time (pulse width) at idle? I'd think 2.5ms to 4ms for an injector pulse at idle should be about right and WOT I would guess 15ms +. Thats another way you could see if the ECM is really compensating for this condition. Honestly it's nice to be able to have someone who understands these terms, having to explain all this can take weeks sometimes.

One last thing I've been doing in past few years is going through the Mode 6 data. If there's something that is close to setting a code but not there yet, it will show in the mode 6 data list, Autel shows a good list of it all. Just look for "OK" or "Failed" in the test results. And even the number is gives for the test result can give you a clue as to what monitor is close to failing its self-tests, it will give a min, or max, and the test result number.

This is an example of the injector pulse tool, this is a cheap one, but they work pretty good, as long as the pulses are even. Here's a video on running the test, if you're unfamiliar with it.
Let us know what you find next. Sorry for the long post.

https://www.youtube.com/watch?v=K7STocr9FBI