I would keep the reactor effluents separate, but yes, you can fill the reactor entirely with sulfur and just monitor alkalinity and adjust the calcium reactor accordingly, meaning you may have to lower the CaRx pH set point to release more bicarbonate from the media, or you can run the denitrator effluent through a separate media reactor filled with CaRx media then back into the sump.
I don't think it really matters where the alkalinity used up by the denitrator effluent comes from, as long as you provide it.
But you need to take it slow when you tune in a denitrator. I would do the drop per second increase until you get to the maximum rate with 0 nitrate effluent, then run just under that and give it time go work on your system. Are you sure you are undersized?