So I guess a little brainstorming wouldn't hurt. If we can ask the easier questions now we might be able to narrow down the probable cause.
Do you have an ammeter on the bike? If so, when you turn on the key is there significant draw?
Another fairly simple one is the condition of the battery leads. Are they all clean and complete? I've had one disintegrate inside the plastic shield so it looks like it is complete but actually separated.
I think there's also a relay in the starter system? Have you tried replacing that? (You mentioned there was a significant replacement of electricals done)
When you consider the kind of draw that you're talking about it should normally blow the fuse if the surge is over the limits (Assuming the value of the fuse is correct for the bike). If it isn't part of the fused circuit then referencing the electrical diagram might point you towards the culprit(s).
Last - sometimes I enter key words on a google search and it's surprising how many other people have had the same issue. like this:
https://xjbikes.com/forums/threads/hot-starting-problem-xj550.47894/Good luck in your hunt.