Just seconding this, it's no big deal to check bags across tickets if need be. The few times I've had to do it on DL/DL tickets, it's taken the agent maybe all of 1-2 mins to add the additional DL leg(s) on to the bag tag. Last time I had to do it, I was at PVR, and PVR-ATL + ATL-BDL was weirdly cheaper on miles than the whole thing as one ticket. Even in a station as small as PVR, the agent added the leg without skipping a beat, so I'd be confident that it'd be a non-issue somewhere as big as JFK.