We serviced out a Dude a few years ago. I don't recall the problem, but it does not seem challenging to sort something like that out. Any transformer that can deliver the current you need should do the job. I'd be very surprised to find out that the filament transformer made any sonic difference at all, as long as you spec it properly.
Is the transformer running the tubes with AC current or is there a DC filament supply? If yes to the latter, I'd suspect a problem with the DC supply.
Is the transformer running the tubes with AC current or is there a DC filament supply? If yes to the latter, I'd suspect a problem with the DC supply.