I was thinking about this circuit and I came up with something for someone who built this for a second time, or someone who is WAY too ambitious (like me).
Okay, so I looked at the argument about 12V vs 9V and I was thinking about using a 12.6V transformer and a full wave rectifier TUBE. Now, this might be too bulky for such a small pedal, but it would kinda be more like a real tube amp... Maybe I'm just crazy... errrr... maybe I'm crazier than I thought I was!
Didn't I also see something about the tube heaters needing (or wanting) 12.6V???
Not to mention, 2 TUBES LIGHTING UP!!!
A 12.6v transformer will not give you the voltage you want for the filaments, unless you skip rectification and just use the AC. If you hook the heaters up in series, anything from 9v to 13v will work, although 9 is pretty low to do the job, and anything over about twelve and a half will reduce tube life. Something like 11-12 is probably ideal. If you're hooking up the filaments in parallel, halve those voltages. A 12.6v transformer produces 12.6 VAC, after that goes through a bridge rectifier and hits filter caps, what you end up with is 12.6 * 1.414 volts, less the drop across the rectifier diodes. In practice, this works out to maybe 16.5-17v, which is high enough to fry the heaters very quickly. If you use a different rectifier topology, you end up with 12.6 * 0.707 volts (minus losses), which might get you 8 volts, with luck. Tube diodes have higher internal impedance than silicon, so the voltage drop would be greater, but I really don't think by enough to drop your 16.5-17v to 12.6 or less.
If you want to do use tube-rectified DC for the heaters, you need a transformer in the 7-9v range (or half that if hooking them up in parallel). Or higher voltage and a regulated power supply. Do remember to get a bigger transformer, since you'll need to provide the rectifier with heater current, too.
Bear in mind that tube rectification's main mojo (power supply sag) does not apply to Class A circuits, which this one is, so the only benefit you're likely to get for the added expense and bother, will be cosmetic. If you want to make it more like a tube amp, there are probably better ways of doing that. You could, for example, use something like a 20k:2k output transformer. This would cut the output at clipping from close to 9v to a more manageable 0.9v, lower the output impedance, and probably make it sound a bit more like the real deal. Since you're very ambitious, I'll leave figuring out how to do that as an academic exercise. It's not hard, and learning is good.