Bi amping with Tube and Solid State

If you ask Linn they will stand for product against removing built-in crossover and they're partially right. On the other hand passive bi-amplification of even perfectly matched amps can drive system out of tonal balance. Volume control in your Mac might help matching but will not help to keep balance due to the complexity of a speaker load connected to two amplifiers.
Without worries you can do it with electronic crossover $500...$1000.

Murph...,

Your suggestions seem to be fine but you're still facing a "double-degradation" using passive crossovers on two sides amplifier and speaker-embedded.

A capacitor tended to bring more distortions than any active element so mainly a lot of engineers try to avoid their introduction unless for smoothing in PS or forward or reverse correction of RF in input and feedback circuitries. A further note that capacitor isn't an ideal and "strong" filter as you may expect and more or less will pass portions of "unwanted" amplitudes in such interaction.

The more complicated part that is not probably covered in EE books due to complexity of calculations and tremendous time to be spent for testing is integrating built-in speaker crossover or actually complexed speaker load with built-in crossover with filters tended to be used on amplifier side.