First, even though I don't know what's up with the amp based on available info so far, I agree with Latole: I would stop using the amp until you have more fully diagnosed the problems and/or taken appropriate steps to fix some of the issues.  Based on the symptoms you have described, you could possibly end up with a blown power transformer or other damage, if you or others keep running it as-is.
Second, yes: it is possible to tear down a PC-board based amp, and rebuild it point-to-point as another model of amplifier.
I've never owned or worked on a TSL100 myself.  So I can't comment specifically on possible success in starting with that particular model and ending up with something more like a JCM800 or JTM100.  But my guesses are (1) you could probably find someone who has done it, using your ol' google machine and (2) it would probably work.
More generally, you can definitely find where people have done similar things - tearing down a PC-board amp, and rebuilding point-to-point.  Doug Hoffman (sponsor of this website / board) has similar projects described in detail, and sells turret boards etc. needed to get them done.  Here is an example of one such project:
https://el34world.com/Hoffman/Blues_Junior_Build.htm