Keep the transformer and the power supply circuit by the circuit that processes the signal is often not sufficient.
In my experience, I learned that it is necessary to filter well the tensions that fuel circuits, both tube and solid state that this is also true for the signal tube filaments (such as our small NOVAL).
On the picture of my avatar you see the two heat sink that mounting the uA7806’s that fueled the filaments of the two 12AU7 (Philips JAN 5814A) of the front end stage (parallel SRPP directly connected to the grid of the 300B, its filament was powered by a LM338K mounted on the rear). And it was a power stage, not signal...
In the prototype of my two-valve version of the Tube Driver ALL voltages are thoroughly filtered and then adjusted using IC's. And I can say I achieved a very good result, although the size stomp boxes will necessarily larger than usual... I do not want to apply a output buffer to my overdrive, but I suggest you try this schematic because in other applications it gave me great results (especially when the jack that connects the pedal to the amplifier is long).