The amp will no doubt have a bridge switch. If you set that, it couples the channels, making it somewhat of a mono-amp. Just plug either R or L input and use one of the outputs for the sub.
The Crossover actually allows you to make two stereo two-way systems with an added sub. Since you don’t have seperate low cabinets (that role is played by the low end of your JBLs (that has a passive crossover – you’d need an extra somewhat smaller amp and modify your JBLs to circumvent that if you’d want)), I’d run my sub on one of the two low outputs (low end is usually mono anyway) and set the filter on the front to 250Hz. Now everything under 250 will go to your sub, everything over will go to the top ends through the high out. While the sub usually works best around 125, it should have no problem handling the extra low to 250. This would make it into a sub/low unit rather than a sub.
Do you have some info on the amp (brand/model would help, as would a link to pics or manual).
Same for the sub. Do you know what frequency it handles?