So in short, there's no way to rectify my current situation with a resistor.No, we haven't said that. Despite all the potential issues we've cited, using the resistor with the paralleled speakers could conceivably still result in acceptable sonics, and as Bill indicated it does seem to be worth trying.
Is there possible to redesign a 4 way crossover so that the speakers can be wired as a series or series-parallel?Not sure exactly what this means, but I think you had indicated that all of the speakers that would be used in each channel were different designs, so connecting any two of them in series is unlikely to result in good sonics.
Or, as a last resort, to use separate amplifiers for each channel.....If you mean using separate amplifiers for each speaker, or perhaps for each parallel combination of two speakers, yes, you could of course do that, as Czarivey indicated earlier. You'd have to make sure that whatever is driving the multiple amplifiers, such as a preamp, or pre-out connections of the receiver if it provides them, would have a low enough output impedance to be able to properly drive the combined (paralleled) input impedances of the amps. Although with most solid state preamps that is unlikely to be a problem.
Regards,
-- Al