I see. I tested the circuit at +/-12V from my “bench supply” and it worked fine. However, I did not make any comparison measurements, so I have no idea whether there was any difference in the output amplitude. Also, during these tests I was using a different pentode (although I doubt this made any noticeable difference).
You won’t be able to run this on +/-12V the way I built this though, because the XL6007 is a step up module, and the input voltage needs to be lower than the output. If you really want to run this on +/-12V with a dedicated supply, you can use a 9V “wall wart” at the input instead, and use the +/-12V version of the XL6007 module instead. Doing so, however, will get you a problem with the LM317, because the minimum drop for good regulation needs to be at least 3V. It’s probably okay to give the heaters only 6V, but then you won’t be able to limit the inrush current using the dropping resistors. Which in turn means, that you won’t be able to use a cheap readymade LM317 module but will have build one yourself, one that uses the extra capacitor and PNP transistor for the “soft start” current limiting. So the +/-12V is actually way more hassle than +/-15V.
As you can imagine, I considered many such options (as well as tubes with different heater voltages, different buck/boost modules, different dropping resistors…) What I presented here, I consider as the simplest/easiest/cheapest option to get a nice sounding and flexible tube module. I can be convinced otherwise though, as I am pretty sure that I might have missed some interesting option!