A while back, I posted the details of how the Rabbit/Turtle circuit works in
this thread. I should have sent you to the thread before, but didn't think of it until now. With your detailed info in your last post, I think we can make some analysis and eliminate a couple of things.
You said you replaced the hi-shift relay. That leaves the low-shift relay, but all it does is provide ground for the high-shift relay coil. If it were grounding out, the circuit would not care since its function is to provide ground anyhow. With that info and your troubleshooting, all that's left is the diode pack, switches, and wiring. You can eliminate the joystick switch by disconnecting it and using only the fender switch. The contacts of the fender switch are open after you set Rabbit, but power comes to the light bulb for Rabbit.
The same power that holds the range solenoid powered is fed through the latch diode to hold the hi-shift relay coil energized. It's ground path is through the low-shift relay contacts to ground (see slide #3 in the linked thread, 1st post). The diodes are in the same general location as the relays under the cowling on the left side below the steering wheel. A diode pack contains both diodes. If one of those is heating up and shorting to ground, it could cause the problem because the diode is before the hi-shift coil and that would pop the fuse.
I know you wondered about this diode pack in the beginning and I played it down, but I think you should probably go ahead and replace it based on your excellent troubleshooting. You just can't troubleshoot something that works for 30 minutes and then shorts out internally unless you feel the heat or see burn marks or smell odor. I know it's a bit of an Easter egg hunt, but if your wiring is all good and not mouse chewed, I think changing that diode pack is the next move.