[jsbihn]

i work on cars like i have always worked on people.... with this motto. if you hear hoof beats, think horses not zebras. meaning, think or do the most simplest first. in this case, i am not sure who did your diagnosis for you but either way i would have started with the most simplest.

usually it is the oil (usually the level or the type), so I would have replaced or checked and filled the oil for the trans. but I would assume that everything was replaced and refilled correctly after you had the trans replaced.... at least we hope.

first i would check the oil level. it just might not have enough oil in it. add some if needed and see if that fixes it. just because a "professional" might have done your swap, doesnt mean it was done right.

even if still, it wouldnt hurt to try changing the oil.
the tranny remanufacturer might recommend a different oil from stock. maybe something a little thicker or maybe thinner. some trannys also might need a break in oil. depends on what your transmission guy does and what he tells you to do.

but based on what you are telling us and the common problem between both transmission....
I would say that the main culprit probably all along.... even before the tranny was replaced.... was the trans oil line or pump.

if the line is blocked, you will not have proper circulation of oil. if the pump fails, then of course the trans oil level will not be correct and there wont be enough oil in the trans to shift correctly. and of course if it is acting like this across two transmissions i would say this is probably more likely.

if you arent getting any CEL lights, could just mean a bad sensor or not.
i have found out that unlike my Vette, these trucks have alot of things not covered under their sensors. My vette has so many sensors and they are all running in sync that if a sensor goes off in the drivers seat (yep there are sensors for the power seats too) it would put the car into "limp mode" or shut it down. Not so much in the H2. I have some minor issues with my H2 and yet no CEL and no codes are registering off my code reader

Anyways.... I hope this helps