Replace starter's solenoid, or just replace starter.
It could be multiple issues but if you are bypassing ignition switch and ignition relay on the fender, then there's nothing else involved except the starter's solenoid. I mean, there is, like the cables, but your problem isn't that you aren't getting power to the starter, it's the opposite.
If starter's solenoid contacts were fused it would indeed happen when you reconnect battery but if solenoid is getting stuck when it's powered, conceivably when you disconnect battery it returns to its home (unpowered position) and thus doesn't run when you reconnect battery.
Just follow what they (guys who know more than me) tell you here. There are limited parts involved and ways to test each of them to isolate the issue.
Maybe you could get a starter, hook it up without installing it and try it... so you could take it back if it's not that... but I think it is.
You could also test to see if there's current going on/off at the connections to the starter (its solenoid). If you operate the key and get current on/off per how it should operate that would tell me it's in the starter/solenoid. If the current doesn't go off when you release the key then you know it's upstream of the starter... doesn't mean something isn't also wrong with starter, but you'd know that much of things is ok (or not).
As to not getting spark, that sounds like a completely separate issue? Fix one thing at a time... might be related but I don't know how - other guys will know if related though.
I suppose you could have an intermittent short somewhere but you would find that out in the tests. The fact it happens when you short across the terminals at the starter tells me the problem, or part of it anyway, is right there at the starter or more accurately probably its solenoid.
It kind of bothers me that things were fine until you replaced the fuel tank. But I have to think this is just coincidental failure, I can't imagine how that would have anything to do with the ignition problem unless something related was damaged in the process which seems doubtful.
You could also take out your starter and bench test it or take to parts place for them to test, instead of getting a new one to test. But I think you have done that test and it says replace starter, to me. Not that expensive, and Advance has one with lifetime guarantee (one replacement). You can replace just the solenoid, but to me, it makes more sense to just replace the whole unit, if the issue is in that unit.