I agree that your transformer has lossy epoxy impregnant. Chuck sells a beautiful drop-in replacement, but it's within many people's abilities to wind your own. I did this for my 453 which had the same problem, and wrote it up under "453 HV Transformer Rewind". The 547 transformer is the same order of complexity. If you like making your own stuff, give it a look.
The 2N2207 is notorious for developing tin whisker shorts. Often it's possible to clear them with a pulse of energy. Note that the whiskers frequently short one or more elements to the case, so start there. What do you have to lose?
In the CRT beam unblanking circuits, the ability of the 2N2207 to generate a large, fast transition is exploited to the fullest, and nothing I ever found matches it. The BC556 and several others can be made to work by speeding up the base drive. I doubt that's possible in the horizontal amplifier; then again, maybe they don't need to be so fast there. You have nothing to lose. If they are being employed in a balanced circuit, replace both sides to avoid Si vs Ge Vbe mismatch. Watch the pinout, it's probably not what you expect.
From: TekScopes@groups.io <TekScopes@groups.io> on behalf of Morris Odell <firstname.lastname@example.org>
Sent: Tuesday, May 28, 2019 3:56 PM
Subject: Re: [TekScopes] 2N2207 replacement in 547.
I'm sorry to say those symptoms are classic for the HV transformer thermal
runaway problem. Unfortunately the only cure is a replacement transformer -
you will have seen endless discussion on this subject if you have been
through the archives. I wouldn't advise swapping the transformer from the
other scope, it's likely to have the same problem if it's an original. You
don't want to go through the complex job of replacing the transformer with
another dud. The only source I know of for replacements is Chuck Harris of
this group and I'm sure he will reply to you. I'm traveling in the US at
the moment so have no easy access to the manual to help you with the
transistor replacement. However you are unlikely to do any harm by trying a
BC556. It's not an expensive experiment.