First, I think you mean the "Largest that will still fit in the overhead," right?
Second, while I don't fly often in CRJs, in my experience, DL and AA are prepared to take your bag on the jetway and return it on arrival. It's not as convenient as having direct access on board but it beats the standard baggage check process. Has this not been working for you?
Third, if you're committed to finding a bag that will fit in the CRJ, note that ebags.com provides size details on all their bags. Next time, take you "doesn't quite fit" bag on board (as if you assume that since it's a legal carry-on that it will fit), hoist it into the overhead and get a good reading on how much smaller a bag would need to be.
You wrote, "I think the rate limiting factor is not the height or length, but the depth." You want to KNOW your size limits.
Finally, don't forget that a bag that just fits in one tail number, for any of several reasons, may not fit in another aircraft, even the same model (CRJ 200 vs 900).