HUH! I learned something new today! Didn't realize that door does not get to the sending unit! I always thought you could access it from there.
I don't have a 1st gen 4R, but an Xtra Cab truck, and had to drop the tank for this very same issue. Actually, I loosened the bed bolts and just pushed the pass. side up enough to get the sending unit out. Was much easier than trying to drop a full tank of fuel.
Also, IIRC, there are two types of sending units, one for the SR5 and one for the non-SR5, I think its because of the SR5 low fuel light, but I'm not positive about this one. Its been 20+ years since I replaced it on my truck.