I will preface this with the disclaimer that I have not bi-amped my 4343's, so my input is purely theoretical. When you switch the speakers to bi-amp, you bypass both a 52mf capacitor and a 2.9mh inductor on the HF side, and the 5.4mh inductor on the LF side. However, the bypassed components on the HF side, I think, function to attenuate the HF side, not as a HighPass crossover. the HighPass crossover is not defeatable, so if you use a standard 250hz card in the crossover, you will have two HighPass crossovers in the circuit (one active, one passive) and one LowPass, in this case at slightly the wrong frequency, and your frequency response hole will be even larger than you thought. JBL's factory bi-amp solution was the
52-5140 crossover card (labeled 4343 LowPass), which did not have a HighPass section - it passed HighPass through to the outputs, though I don't know if it had any attenuation. I think it was 275hz LowPass only, 12db/octave. In your case, you could approximate this by splitting the fullrange output of your preamp and sending one leg through the crossover for the LowPass (woofer), the other straight to an amplifier with a gain control for the HighPass (MF/HF/UHF).
If I'm wrong on this, I welcome corrections