IMHO Mr. Karston is right about this: "But here’s something to keep in mind. If you don’t have an electronic crossover, this means that all frequencies are being fed to both amps"
I happen to use an electronic crossover made by Marchand Electronics; it allowed me to finally and completely resolve the problem of using a subwoofer with large 2-way speakers with no bloat or redundant amplification of certain frequencies. This unit is relatively compact, very transparent acoustically, and perfectly well behaved. There are other models that would readily allow you to cross over the signal at the required 550 Hz. You would have to choose the slopes for this (I used 24 dB/octave), but that is something the speaker manufacturer might comment on better than me.
It also would be better if both amps are relatively similar in gain. The electronic crossovers I’m familiar with (Marchand’s and others) have gain pots per channel, but the range is not nearly as wide as found in a preamp gain pot. These pots are typically +/- something lilke 6 dB total, and thus should be regarded more as "trim pots" than volume pots. All to say if both amps put out (for example) 26 dB gain, the crossover has to do less (if any) gain adjustment, in addition to division of frequencies fed to each amp.