Introduction, and trans issue

It sounds like it had very little to no throttle pressure if it shifted that soon. As such, it could have damaged the transmission. Chrysler products are not like Chevys. Chryslers MUST HAVE that linkage connected, or the transmission will burn up, beginning with high gear, then second and finally first. The reason is because without that throttle pressure linkage, the clutch packs don't have enough pressure to hold the clutch packs together as the vehicle accelerates. That's the whole premise behind the linkage. To make it increase as the accelerator is depressed further and further. Here is what you need to do. "Whatever" you have for that linkage, whether it's linkage OR a cable, you need to adjust it as follows.

Block the gas pedal all the way to the floor, without the engine running of course. lol Next get under the car and locate the kickdown lever on the transmission. Grab it and see if you can push it BACK towards the rear of the car. If you can, you want that lever adjusted so that it is all the way back with the gas pedal on the floor. Once adjusted like that, drive the car and see if it improves. Sometimes, adjusting the lever all the way back is too much and you need to back it off a little to get the shifting where you want it.
I have done what you suggested, and it seems to be adjusted fine, maybe an 1/8 of play to the back left but I think it is ok. Do you think I may need a heavier spring for the selenoid down there?