I would give it a try. At thee same time I'll be getting a tube amp in a month or two. I'll try to see if I can mitigate this problem with that.So my suggestion of adding an extra volume control, downstream of the tuner, would probably solve the problem. Really, it might even be solved just by having a series resistor that could be bypassed for "loud" and inserted for "not loud" modes. It would be simple enough to consider experimenting with the idea.
But I do suspect that it is lack of DC restoration. Loud passage might be creating negative bias and clipping out. But when I reduce the level set the negative bias is dissipated and audio is getting restored. I need to check with a scope and also the resistors too.