It might pay to check all the electrical connections to the trans. Starting with the Range /MLPS switch. MLPS =Manual lever position Switch. It just possibly could be a faulty connection where the trans isn't getting the signal to energize the reverse system.

 

I have a 91 ranger different trans but, I was told mine was shot, However I changed the fluid, replaced the two (servo's) on the outside of trans($20.00) each, adjusted the linkage,"the correct way with weights". and replaced the Govenor in the end of the trans, then about 200 miles later replaced the fluid and filter again. That was 2 years ago, runs fine. Now I still would not go on long trips, but I probibly can. Oh yea I put a larger trans cooler on it. and did this all with trans in!
With your situation I would say, if the fluid and filter has been changed already, Change it again after 200 miles. Because the first change loosens the stuck on gunk in the trans, it needs to be replaced again!! make sure you use the correct fluid!!! important. maybe a small bottle of lucus trans fix. If you have a small 7" by 4" trans cooler, put a slightly larger on, in its place. Not a big one, this may cause over cooling in the winter!!!!!. also you may want to adjust the linkage, not hard, you can find how online. Oh yea, I don't think you have one on yours, but if you do replace the Vacuum modulator. You should be good if it rus ok for a week or two. I don't know about long trips, thats up to you. P.S. I also know someone who has a 95 explorer I think may be the same trans, he has a speed sensor on the end of trans which causes shift problems, he has over 200,000 miles, hes a old guy who doesn't want to fix anything and has been driving it in 2nd gear for two years!!! If you replace the speed sensor bring the old one in, there are several different sizes! good luck.