[morzh]

It is rarely that a transformer will develop a case of "1/10-resistanseism", it is likely to be open or have a turn short (one or a few turn inside develop a short across which defeats the transformer physics, at the same time your DC resistance measurement may look OK).

So it is a good chance that like you said someone put a replacement inside.

SIgnal tracer is not a bad idea either. It will allow you to pinpoint the stage where the distortion occurs. Of course scope allows to see WHY it occurs. But then a tube stage is a simple one so once you know where it is, it is only so many things that could go wrong with it.