In reply to:

but there would be two different circuits from different power supplies (two different amps).

You used the term bi-wire instead of bi-amp. You're refering to using one amp to drive each speaker (or one amp to drive each of the sections - tweeters and woofers) which is where I think this got off track.

Bi-wire - one amp, two sets of wires.
Bi-amp - two amps, two sets of wires.

Bren R.