It seems that you have already figured things out.
I, for one, used a powered mixer (Crate PCM8-DP) for years (in the 90's) as my band's mixer.
As my need for more power/coverage increased, I bought a Rane AC22 crossover and a QSC power amplifier to run a two-way system (hi/mids and subs). For routing I went from the "post EQ out" to the crossover, then to the power amp and used the internal power amps (of the Crate) for monitors. Totally flexible system however it was mono...which is fine.
I have always tried to bring what I need to a gig rather than bringing a canon to a fist fight (a pun..).
I did not check the specs on your amp's crossover but you may want to try to use it as an external crossover is a a good visual way of doing it but having "another thing" in the signal chain adds another possible point of failure....just my opinion.
BTW: Although my rig has grown over the years, my trusty Crate powered mixer always makes a trip to the gig - just in case..