Bi-wire v's single with jumper leads.

EMF interaction between speakers is aided by the fact that output of an amp is separated from the speakers by inductance of the cable. Typical wire has inductance in order of 0.3uH/ft - equivalent to 0.188 ohm at 5kHz (counting 10ft both ways). It is 43x less then speaker's impedance but it is only -16dB of power. (our hearing is logarithmic). In addition amplifier's output impedance is in the similar order at 5kHz (or even worse).

How do you figure the emf of the LF driver (essentially a source at that point) sees a Z of the cable and amp that is less than the Z of the HF circuit? It is not even close. HF circuits typically have a resistor in series with the driver ( 2 or 2.5 ohms usually), that series resistance plus the R and L of the HF coil swamps the Z of the cable and amp. Additionally, the frequencies supplied by the LF driver that will fall in the passband of the HF crossover are attenuated by the passive components in the crossover of the LF circuit, particularly if that crossover is higher than first order as part of that crossover will have a low Z path that shunts the higher frequencies.

Not every HF circuit has resistor in series - it depend on speaker design (many have L-PAD). I didn't say that impedance of the cable is comparable to speaker's impedance - it is in order of 50-100x lower. What I'm saying is that it might be still audible since our hearing is logarithmic and ratio of 100x is only -20dB of power. Crossover attenuates - but is far from perfect especially around crossover frequency.

Resistor in series (often in L-Pad), that you mentioned, might have something to do with the fact that some speakers show improvement (usually more air) when bi-wired but other don't. It might also depend on the inductance of the cable. Inductance of straight wire is in order of 0.2-0.3uH/ft (depend on gauge) but my interconnects have only 40nH/ft (I don't know how they do it)

Even if you divide mentioned effect by another 100x it will be -40dB of power and far from being inaudible. Remember we're talking slight difference.

Kijanki: I had misread your earlier post - you did indeed remark ( and correctly I might add) that the cable - amp Z was less than the HF circuit Z.

Musicnoise - This is just hypothesis and changes are so miniscule that it's
difficult to make sense of it. My speakers show slightly more air in the sound
when bi-wired but now I'm not so sure if I made right decision buying shotgun
cable. It costs practically twice and I could get better cable for the same money.

Another strange thing that somebody mentioned is leaving one of the jumper
brackets in-place (one on the ground side). For some reason it made sound
with my previous amp slightly more coherent/focused. It worked only when
jumper was on the ground side and since I have right now class D full Mosfet
bridge driving my speakers there is no ground side and I haven't tried it again.
From engineering point of view it doesn't make sense at all.