Before going much further, you may need to ask your friend something about the power of the parallel-SE amp you built him. Does he need more power (more volume) than that amp, or is he only looking for less distortion (at the same or similar volume)?
If the overall power level is okay, you don't need to build an entirely-new amp. You could just modify what is delivered to the 6L6 output stage (by changing the preamp).
One potential pitfall of both the Double Six and the Standel Puzzle you've assembled is the Bridged-T filter. On the Double Six, this is between V1b and the output tubes and is made of R15, R16, C13, C14 and the Middle control (usually a fixed resistor when the bridged-T is used in, say, Gibson amps).
The Bridged-T filter imposes a set mid-range cut, somewhat like fixed settings of a Fender blackface tone stack. The Middle control in the Double Six will vary how deep the midrange cut is, though it may not eliminate it entirely (I'd have to build or simulate the circuit to know for sure). If it's designed well, that mid cut is right between the Treble and Bass ranges of the James tone circuit between V1a and V1b.
Just something to keep in mind.
The Double Six has only 2 gain stages, with 2 stages of tone control (cutting). That seems like a formula for clean, though I haven't built or heard the circuit.
I don't know if it is similar enough to the existing parallel SE amp you built to just be a matter of dropping in this preamp circuit to try. That looks like an easier path than building the Standel (a push-pull amp with new-everything). Which is why I asked about your friend's perception of whether the overall power in his amp is enough (allowing a preamp change).