Heater still not working

I am not convinced that this is not a heater core but there are things that make me question it. Namely the inlet and outlet temperature of the heater core. Normally when it is blocked you have a cold return line. However, we could still have a partially blocked heater core.

I would suggest we remove the air temperature door and manually move it to full hot and hold it there and check your temps again at each vent. I suspect this may be the issue just because you have 168 coming into the heater core but your air temperature is only 118 at the hottest. I anticipate a drop in some temp but not 50 degrees. You may need a helper to do this but once you remove the motor you will be able to move the door with your fingers and put it to max hot. It is full travel one way or the other so just test it in both directions. If you don't get proper heat that is pretty even across all the ducts then the heater core would have to be the issue.

Sorry. I meant to include that process. Here it is from the manual.

That car uses a parallel flow heater core so you would get good coolant flow through it even if 90% of it were plugged. From the description I would say that you have 3-4 open crossover tubes and the rest are plugged similar to what I put on the image of the core. The coolant flows in, goes across the blue area just fine but the core is blocked from the red line back so no coolant flows through those sections. You get just the heat the small area produces and it will be the hottest air closest to the core, just as you have shown. Totally normal for a plugged parallel core to show the signs you have.

The problem with them is flushing really doesn't work very well because the flush takes the same path as the coolant. I have had limited results with an air and water flush gun and using vinegar to cycle through the core in reverse flow but even then it wasn't real great. The air helps by causing turbulence in the cleaner in the core and gets it in farther to dissolve the calcium and crud. In the end the best solution is usually replacing the heater core.

Yep. Looks like it is moving through its full travel. Normally they have a gear and are not visible but that is pretty clear.

Which takes us back to the heater core. As Steve said these are multipassage so you can have a partial blockage and it causes this issue. The coolant and your flushing will take the path of the least resistance and not remove the blockage.

I have not tried this on a Honda but on some vehicles you can remove the blower motor and see the heater core. If you can, you can use that laser temp meter to see if the entire surface of the heater core is even. I suspect you will have some cold spots which shows it is blocked.

Yes, most of the newer vehicles are a bear when it comes to replacing the core. It's why I always at least try the flush gun on them first. I know of a couple shops that have been trying different methods of using flexible tubing they feed into the core through the hoses with right angle nozzles on the ends and they use those to try blowing the crud out like a sewer cleaner. I haven't tried it yet but in theory it would work as long as the blockages were in the outer tubes. Plus it may give better access for the cleaners to get into the smaller cross tubes. Just not testing it yet, I'd like to try it on a few bad cores out of vehicles first.

The lower air flow is enough that it still heats the air through the section of the core that's working. As you increase the blower speed the air flowing through is more than the plugged core can heat up so it gets colder as the airflow increases. Think of it like you are putting your hand over a flame. If you just put your hand there and move it slowly you get burned, however if you wave your hand rapidly through the flame you only get slightly warmed. Sorry to say it still sounds like the core is plugged partially. If you have access to compressed air and a water hose then you might try reverse flow flushing with a tool like the OTC 6043 or Sealey VS0044 Those use air and water to create a lot of turbulence in the core and possibly free up enough of the crud to get better heat.
This should explain it better as this truck has the same issue and show the process of using that style flush tool.
https://www.youtube.com/watch?v=1R0hVEFZgrw

It's one of the big pitfalls of the parallel flow cores. However it's also the reason why the radiator is a parallel flow design. If you had a serpentine style radiator and any part of it gets plugged you get no cooling of the item attached and it would soon overheat while the parallel flow design will tolerate some flow reduction and still provide cooling. I've tossed together a flush system like those out of plumbing parts before. One thing though is that you want to keep the air pressure low, not more than about 20 PSI or so. That way you don't suddenly cause damage to the core. Back a while I drove a vintage truck that had a bad heater core, but nobody made a replacement for it. I rigged up the heater from a bus and plumbed it into the factory ducting through the blower motor just to get heat while I worked on making a different heater box that could fit an available core.

This is some of the things you will be facing. That crimped area may not effect an air style flush tool as much but it won't help any.
https://www.youtube.com/watch?v=PRSlgj-lmIo