The only perceivable "gap" in your list of cartridges is between 223 and 270. I think a lighter recoiling 6mm, .257" or 6.5mm bullet launcher would fill that gap nicely. I don't know if you reload, as that would determine which cartridges would be suitable candidates. It would also depend on what your intended use is: target or hunting? If target, the 6.5 CREEDMOOR seems like a good candidate in a heavier rifle, would also make a dandy chambering for a lightweight hunting rifle. Of course, for the hunting rifle the list of possible chamberings is bigger: 243 WIN, 6mm REM, 257 ROBERTS, 6.5 CREEDMOOR, 260 REM or 6.5x55.
Anyways, it sounds like a fun problem to solve!