Crossed Posts 
Just so we can see whats involved here is the schematic for the Marshall Lead12-12W: https://www.thetubestore.com/lib/thetubestore/schematics/Marshall/Marshall-Lead12-12W-3005-5005-Schematic.pdf
My first thoughts are to use better RRIO opamps, so that the supply rails could be lowered and get the same or better dynamic range and open loop gain. That would possibly enable a simpler circuit with a better performance, including a lower noise, not that noise is an issue here.
A 12V, 15V, 18V, or 24V wall wart should do nicely for the PSU.
Thanks for posting the schematic, should have done it myself in the 1st post.
I'm still not sure how I could use lower power rails without significantly impacting the way the amp will perform. The thing has 80dB of voltage gain (with the gain pot at max) and the gain pot is part of a low pass filter so it changes the frequency response of the amp. So if the original one clips at 50% and mine clips at 10%, they won't sound the same. At least I think so.
Also, a 9V supply is pretty much a requirement, since this will be a guitar pedal and most pedal power supplies are 9V 
No probs posting schematic

If you have a RRIO opamp, the output will swing to the positive and negative supply rails. With non RRIO opamps, like in the Marshall amp, the output only swings to within approx 2.5V of the supply rails. There are other aspects too, but not necessary to go into that. Just to give and example, using +-15V rails a TIL072 will produce a maximum output of 25V peak to peak, whereas an OPA191, for example, will produce 30V peak to peak. So for the same dynamic range as the TIL072 you could run the OPA191
at +- 12.5V rails.
About the circuit sound, I get your point 100%. I was forgetting that this is a guitar pedal where the sound of the circuit is most important. The TIL072 is sweet sounding opamp, even in clipping whereas the OPA191 would give less distortion, but it would be much harsher in clipping.
I find all the above posts very interesting and, after all the discussions, can I summarize that the specification is to clone the Marshal circuit exactly, to get the same sound. This includes +-15V rails. The power input to the circuit must be 9V DC to be comparable with standard pedals. I think you actually said most of this in your original post.

As well as the opamps, other factors affect the sound. These include: type of capacitor (especially), type of resistor, and the way that the supply rails perform dynamically.
One suggestion is to use turn-pin sockets to mount the opamps. That way you can do opamp rolling if you ever want to. To use surface mount opamps, just mount them on DIL headers that plug into the socket, like standard DIL opamps.
To summarize then, all you need from us is an approach to derive +-15 rails from a 9V input.
I would strongly recommend the use of symmetrical split supplies, for the reasons so well put by Benta in reply #1
One question, and apologies if this has already stated, but will you be running this pedal from a 9V PP3 battery?