Mentioned already above. Before changing anything, I would propose ENFORCEMENT of the current rules:
1. Strictly enforce carry-on rules (it has to fit in the sizer) regardless of class/status.
(FT will still welcome the rants 1) "I have ALWAYS flown with my Tumi model XYZ but was forced to check it" 2) "Rude agent made me stick my carry on in the sizer" 3)"I know my super dope Travelpro xyzlite fits in the 77W overheads bin but was forced to gate check it". etc/_
2. Strictly enforce boarding process
3. Strictly enforce what the overhead bin labels say "Reserved for Business/PE, etc"
In addition to the above and to the size requirements, a weight restriction could be imposed(no exception but J/F/PE) for carry-ons. Enforce it or pay at the gate. Problem solved.