2000 Other Mitsubishi Models COLD hesitation, stumble

Mitsubishi mirage 1.5l california emission 5 speed, minimal problem noticed/started at 60000miles and got progressively worse. At startup from fully cooled (8hrs+ off), car starts fine with key and idles, BARELY touch the gas in 1st to get on the road and it stumbles, it will have just enough power to roll the car but it won't stall. Release the gas and it will idle again, chugging along the road at idle speed. As soon as there's a load on the engine, it will stumble without power to accelerate the car. Give it a minute and it will work ok, but have some stumbling on acceleration. After it fully warms up it is fine. This car never had an intake air control unit thing. No active or pending trouble codes. I have a big clue I think with the following: I live on a hill and can roll a half mile without turning on the car in the morning. I put the key to "on" and then coast 1/2 mile before putting it in gear and pop starting it while rolling about 30-40mph in 4th or 5th gear. The engine will not work, specifically, when I touch the gas pedal I feel major stumbling (no acceleration at all) no change even if I floor it, and if I step on the clutch, releasing the engine, it will stall. In other words, the car will not push start when cold, as if I have no gas or spark. But if I use the key at this point, it will start and idle perfectly, but still get the "regular" stumbling on acceleration as usual. Here's what I did so far in the past 2 years: NEW: oem spark plugs, 2 o2 sensors (california car), new pre-cat, 2nd cat is clean (light shines right through), fuel filter, fuel regulator, air filter, clutch, pcv valve, oil changes (of course), timing belt, battery, alternator, exchanged pcm from an identical car with 50k miles (same exact problem, no change after swapping pcms), removed and cleaned intake manifold, removed and cleaned throttle body and idle air control valve, removed and cleaned EGR valve and fully cleaned the exhaust and intake channels that run to it. (EGR channel runs through the head to the 3rd cylinder exhaust port, this was 95% plugged 1 year ago, it was scrubbed clean through and through), coolant temp sensor, air temp sensor, distibutor/coil, throttle position sensor, compression tested all within 5psi of each other @ 170, fuel pressure tested fine (forgot value, but it was the right amount at cold idle, I didn't check when the stumbling occurs though), new crank position sensor, fixed the common problem of worn crankshaft sprocket for timing belt by wedging feeler gauge pieces in the keyways to reorient proper TDC (got much more power and 4mpg after doing this, but still had same stumbling problem when cold). I am at my wit's end. Please help. The car gets 35 mpg around town but is dangerous when getting out of work's parking into oncoming traffic. I occasionally get oil fouled spark plugs (not always, not sure why), and when I am running a tank with bg44k, the problem doesn't seem to happen as much but is still there. I tested for vacuum leaks using a propane torch all over the entire intake area, there are no air leaks. I sent all 4 fuel injectors to witchhunter. Com for cleaning and testing, seemed to help for a week, then happened again. I often shut off the car and coast down long hills in neutral when travelling and it never has a problem pop-starting when warm, it's only when cold when there's a problem as detailed above. I am leaning towards oil leaking down intake valve guides and sticking to intake valves and will be getting an oil catch for the pcv valve this week, but I am not optimistic.