'I'm convinced its some form of peculiar induction between the electrics and myself.'
Rule yourself out of the equation and play it naked..... alone!!!
Mismatches between instruments and amps usually reduce volume and doesn't create hum but if your fretless works on other amps and not yours then it may be something to do with mismatch. Your headphone amp may 'match' your fretless better or its relatively low gain may not reproduce the hum.
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sj