I haven't used E-drums in a while. What about lowering the sensitivity on the rim trigger? One option you might not have considered; use a real snare drum
I got great results going hybrid with real snare, hat and sometimes all real cymbals(the overhead mics just added some "air" to the overall kit sound). You could also put up a mic and get one of those cross-stick blocks
One other option, if you print drums to audio(which I always did), I would add a blank audio track below the snare track, separate the cross-stick audio and drag it to its own track. That also allows for different EQ and reverb
