I was going to say "excellent first post" but this is an excellent post whether it is the first one or not .Now that is funny. Design process is a constant battle between mutually exclusive goals. You have to ultimately choose priorities and make tradeoffs.
Normally any speaker crossover with a rolloff steeper than 6 dB per octave will warp phase and screw up time alignment. That's not a fatal flaw and most speaker designers accept this in return for the advantages of steeper slopes. There may be a high-tech solution with digital signal processing, but even in the digital realm you typically get the same phase warp as with analog crossovers. There is a software app called "phase arbitrator" designed to reverse the phase warping of a DSP crossover, and probably some other DSP tools with the same goal.
Welcome to the forum.