Sorry to hear about your troubles. Some 3rd gens are good and some don't hold up as well.
My '02 is now past 80k mile mark and I have never had any repairs done to the drive train. My 5R55W and SOHC have never skipped a beat. Never had a slightly delayed shift, rough idle or whiny rear diff. I contribute this my vigilant maintenance.
I run full synthetic oil in my engine, which reduces start-up wear almost 10-fold compared to convention oil (more than 90% of all engine wear happens during start-up). I do an entire flush and filter change to the 5R55W ever 15-20k miles and change my rear differential oil ever 15-20k miles with Amsoil heavy gear oil. Or once every year, which ever comes first.
With my proactive regimen I hope to reach 200k miles before having to even touch my SOHC or 5R55W. Only time will tell I guess.
There are a few people on this forum that have claimed to achieved well over 100k miles on their original 5R55W.
here,
here,
here,
here and
here.
I think the secret to these years explorers is just vigilant maintenance. I just think the deal is that you just can't get away with the same maintenance on these 3rd gens as you could on the previous years.
My 3rd gen has taken me all over the state of Texas, Oklahoma, Nevada and the mountains of Colorado in every weather extreme you could think of and wouldn't hesitate to take another expedition across the states again if I had to right now.
Perhaps the previous owner of your ex abused it through lack of maintenance/knowledge. But know you know how to maintain yours after you get it all fixed up!
I just had the door adjar issue. There is no button in the door jams, it is in the latch of the door. I just had to spray some oil in all my door latches to fix the problem. I do this yearly and have never had the door ajar issue come back.
Just wanted to encourage you that these can be made reliable through proactive maintenance. Good luck!