Might be a pain due to the distance for wiring, but what if you went with the drywell route with a sump pit on top. Stick a pump in this area to handle the overflow when the drywell can't keep up.
I'm not sure what you mean by wiring. The check valve would be a rubber valve connecting to runs of 1 1/2 in. PVC discharge line. I just don't want to create another issue since I don't know if this is possible. I'd spend $10 on a check valve if I know something is going to be damaged by my attempt.