Could you share the schematic?
I've always wondered about tubes in pedals -- what kind of power supply is needed, etc.
I don't believe this is what you're looking for, but the schematic (and kit, if you prefer) can be had here:
https://www.amplifiedparts.com/products/effects-pedal-kit-mod-kits-persuader-deluxe-overdrive.
The tube runs on 9 volts and breaks up almost instantly when a signal hits it because there's practically no headroom. This is nowhere near a new concept - there's been commercial pedals over the years that do the same thing.
If you're gonna build one, I encourage you to buy what parts you can from
https://hoffmanamps.com/MyStore/perlshop.cgi?ACTION=enter&thispage=partsenter.htm&ORDER_ID=!ORDERID! for giving us this fantastic message board

.
But on to your real question, the tube pedals I've seen are normally powered by a step-down transformer used in reverse. So, say you took a wall wart transformer... it gives you 9 volts at 500ma, right? Feed 9 VAC into the step down side of the transformer and you get 120 VAC out the other side at around 37ma which is plenty for a 12AX7 (It also voids the warranty on your wall wart

). That is the transformer only, not the whole wall adapter circuit. This would allow you to build just about any tube preamp circuit you can think of and slap it in a box. Hammond has a ton of different mini transformers which are well suited for said application.
I also read in a book by Nick Boscorelli that he uses an op-amp to achieve high voltage. It can also be done with a transistor and timer IC running off of DC. I have a copy of it here somewhere and if you're interested, I'll try to dig it up.
Each way has plusses and minusus. Transformers are kinda big and require DC-AC conversion or a dedicated power supply. Op Amps and transistors get hot. Most of this is still theory to me and I'm still learning myself. Hope this helps a little tho.