Alright, I tried to remove the input tube and then checked again. Result: No more hissing and crackling with the input tube removed. I guess we can safely narrow it down to the input then?
I didn't know either that the tube could be removed safely while the amp is running. Also, I managed to keep the burns to a minimum - the input tube gets much less hot than the other ones. I guess with some gloves you wouldn't even feel a thing. Real men use their bare hands of course.

Anyway, how to proceed? Steve, do I have your permission to open up the amp and take a look inside? Just making sure, I don't want to void my warranty.
If it's just a bad solder joint on the tube socket I should be able to fix it - I do know how to solder and have the equipment - but if it's in any way related to the electronics I'll stay away from that. In any case I could take a few pictures of the inside and check if there's anything nasty.