I can propose a potential explanation for what is happening electronics-wise as well as sonically.
Firstly it probably comes as no surprise to Bottlehead forum members and owners that vacuum state electronics differ from solid state electronics in their overload characteristics and tendencies. Specifically, tubes can swing a lot of volts in comparison to ss small-signal devices.
But how can that in turn result in a cleaner overload character? One at first assumes that the power amplifier has a certain sensitivity and a certain output power at the onset of clipping. We test power amps for these very characteristics and conclude the power output specification from them.
Let's assume that no genie arrives in the sound room and the mere presence of a Bottlehead preamp in place of a different Solid State (SS) preamp does not change the steady state power output of the power amplifier, nor does it affect the transient state (dynamic "music power") capability ... if the power amp was capable of clean transient output in excess of it's steady state (sine wave) output, that nothing changes here and the same short term ability remains unchanged.
However we do need to assume there is some ability of the power amp to produce good transient behaviour. Some amps are good for so many watts, fast or slow, and that's that. We are assuming that we are not running such a power amp.
What, then, of the preamp's transient abilities? There exists some (not enough, unfortunately) evidence from testing that vacuum state small-signal and power devices can swing significantly more voltage in short term transient signals than even the already impressive overload characteristics of a typical tube preamp. I've seen some where the output of a tube amp can be 3 or even 4x the sine wave pre-clipping output over very brief periods.
Now, this is not a unique feature of VS (Vacuum State) small signal components ... SS preamps also have transient abilities. It's just that the SS devices tend to be on the order of 2x or less than the steady-state output abilities.
I think your Bottlehead is throwing a lot of clean power to the power amp, the power amp is capable of dealing with it cleanly provided it's not too long or doesn't repeat too fast for the power amp's power supply to recover, and this is in contrast to your old preamp that would not be able to do the same.