A few key points on the 1988 starter, and I took some liberty with your post for some other indications...
The '88 & '89 starters all have TWO lugs unless the starting system has been modified. The case of the starter is NOT grounded for these years. In operation, starter Relay "B" for the '88-'89 years would provide a switched ground to the starter through the second lug.
How many large gauge wires were attached to the starter you removed from your 1988?
It would be helpful to check the performance of Starter Relay A (large solenoid just forward of the battery) by measuring battery voltage on the large-wire connections (one should be full time 12V and the other see 12V only when cranking). Also, check the performance of Starter Relay "B" (larger solenoid just rearward of the battery) it should switch a ground and ONLY if Starter Relay A is functioning.
Post back with what you find, and I'm sure we'll get this solved for you.
A few notes:
- Everything here assumes that your battery, all wires, and connections are in perfect shape -- something that I don't see was tested on the bike - you mention that the "hot" wire to the starter dropped to 2 volts - what was the battery output and the voltage on the two posts of Relay A? Also, what were you using for a ground reference? If not the battery's negative post, you would need to measure the cable connecting points for all of the Relay B ground circuit as well. (As posted, a weak ground and Relay B not switching because the reverse gears were partially engaged could produce the 2V measures if you were using the engine case or bike frame for ground reference)
- If Relay A works and Relay B does not, Check the 5A fuses in the rubber cover near the negative battery terminal and ALSO verify that the Reverse Switch (the 'stud' type switch bolted into the right side of the block kinda below the reverse shift cables) is providing a good ground -- the 5A fuse is in the positive side of Relay B's coil and the Reverse Switch provides the ground... a lot of people blow this 5A fuse when jumping or charging their bikes...
- If Relay A works and Relay B is also working (switching), then run your starter to the local auto parts store and bench test it there -- Looking from the rear of the 2-lug starter with one lug pointing nearly downward (5 o'clock) and the other lug in the 2 o'clock position (similar to it's installed orientation) the Lug in the 2 o'clock position would be positive and the other negative. Have them measure the current draw on the starter and post what they find.
The Starter system on your '88 has a boat-load of safety interlocks to keep you from starting in unsafe conditions for both you and the bike. Given that this bike has been sitting a while and that you've had it only a month, we may be chasing something sticky or dirty in those systems, so it'll help to keep an open mind.