Practically speaking, the method you suggest will indeed work as well as any.
Technically speaking, there's some theory to be known about crossovers to get an even amplitude- and phase response, however if you're anyway going to EQ (which deliberately changes the amplitude response) and re-amp (which completely changes both amplitude and phase) then there's no point in being pedantic about the crossover. You may get phase cancellations near the crossover frequency, and because that happens to be a quite crucial region for bass it's probably a good idea to fine-tune the phase relation there. To do that, use in addition to the LPF/HPF also an all-pass filter on one of the tracks, somewhere between 200 and 400 Hz, and play around with the exact frequencies of the three filters until you have the subjectively best sound.
An alternative is to use FFT-based FIR brickwall filters instead of the standard IIR-based ones you find in normal EQs. That precludes phase cancellation between the partial signals, but it won't necessarily give a better final result – such hard FIRs kind of butcher the transient response, probably not something you want for a rhythmic bass track, and you may still get phase interactions between the overdrive-induced harmonics of each track.