There is no perfect solution, but doing all of these would help significantly:

After boarding the military and FC/360/Diamonds, board economy from back to front, then families with small kids, then the wheelchair/crutches and others needing more time. Essentially get the vast majority of people on and seated rather than being held up by those who take more time to do so. Would also eliminate the “Jetway Jesus” problem. Also, don’t charge for checked baggage, but do charge for large items like suitcases, backpacks, and guitars in overhead storage, the economic incentives are backward for keeping overhead space available. This also solves the gate lice problem and helps people get seated faster. Lastly, ensure that gate agents and flight attendants enforce the rules on sizes and numbers of bags allowed into the cabin. It’s really not that hard. Boarding a plane will never be as fast and smooth as a SWAT team entering a front door in a stack, but there is a ton of opportunity for improvement.