For the Aylesbury line, I'd go for 4-rail electrification for all tracks parallelling the Met. I reckon there could be a good case against the extension ban, on the argument the new ground level conductors would be close to existing fully segregated dc tracks and introducing an additional high-voltage system in the vicinity would actually introduce more risks and challenges overall than the alternative method of decarbonising and local particulate and Nox emission reduction. The Marylebone approaches, largely through tunnel and also totally segregated, could be argued as a justified rational short extension of the 4 rail method to the terminus. If that was frowned on, then on-board traction batteries could cover the run into the terminus, batteries that would be required anyway and sized to cover the Aylesbury run north of Amersham, with some automatic fast charge top-up capability at the outer terminus berthing points.
For the High Wycombe line, 25kV OHLE all the way, or at least as far towards the stops as possible. It could coexist amicably with Aylesbury line 4-rail from Neasden to the terminus if so desired. If overhead conductors in the tunnels prove impossible, then on-board traction batteries could, again, be provided on the AC units, sized to cover the discontinuity, or if 4-rail was able to be provided throughout this area, then dual voltage capable traction could be used.