Bi-wire v's single with jumper leads.

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.

I'm reading a bunch of stuff in these posts that doesn't make sense. The reason bi-wiring works is due to the finite but definite level of resistance a wire has. If you send a current to the tweeter and woofer and the crossover splits it and then the signal returns via the "ground" speaker wire. That return post from the crossover will develop a voltage. Because the current is flowing through the wire that has a resistance. Bi-wiring improves the sound because the tweeter return path is on it's own wire and therefore the voltage at the crossover is due only to the tweeter current and you will not get intermodulation with the current flowing through the bass wire (the voltages sum when using one wire for both). The net result is that the larger currents that flow through the bass network do not affect the amplitude of the tweeter signal.