do you mind to elaborate on what you meant when you wrote preserving the damping factor at crossover frequency
When using active crossovers - which entails removing the passive in a multiway speaker - the amplifier is connected directly to the driver, so the damping factor of the amplifier is unaffected.
An idealized passive crossover has an infinite impedance at the crossover frequency. Hence zero amplifier damping. In the real world, the impedance is not quite infinite, but can be several multiples of the nominal impedance and thus driving the damping to zero. Look at speaker impedance graphs on Stereophile and you will see impedance peaks of 10x nominal. The phase response is horrible in the XO region.
Thinking of budget I would forego xo to the Mains. And thinking about the high level input the question arise if the the worse tube amp bass performance relative to solid state is due to interaction with speakers is it then less worse going into the subwoofer. If tubes mean bad bass then I would also have to forego high level input .
XO to the mains is trivial. A simple series capacitor correctly sized to the main amp impedance. Anyone can build one in an afternoon. XO frequency should be at least ½ octave above anechoic corner frequency.
High level sub inputs are about the dumbest idea extant. People spend silly money on fancy speaker cables and then gum up the works with a "Y-cord"