Would it be possible/recommendable to use a 270K at the input of the S.E.X. circuit, instead of the stock 100K?
No. The value of the input pot is a compromise - higher resistance provides less load on the source device (good) but it also increases the influence of the Miller capacitance of the power amp's driver grid (bad). In most cases, 50K to 100K is a good compromise.
For the SEX amp, a 270K input pot set at -6dB (worst case) would give a treble rolloff of -1dB at about 13kHz, and -3dB at 26kHz. Many designers prefer to keep the -3dB point at 100kHz whenever possible, on the grounds that more subtle but still audible effects occur before the measured frequency response is compromised. I think this more stringent rule of thumb is situational - sometimes important, sometimes overkill - but it's not a bad guide in general.