Here's my completely uninformed unsolicited hot take:
Prior experience hires should face the same initial cap as Academy grads. Force the agency to truly staff the lower-level facilities to 100%+ and allow them to release to the higher facilities.
Initiate some sort of scale where higher-scoring Academy grads can get to higher-level facilities, and/or let people who score below 70% (say at least 55-60% maybe?) go to Level 4/5 facilities. The final few Academy problems are like Level 9 traffic, people work those problems and then get placed at backwater facilities that never see a tenth of that... seriously, a brain-dead monkey could certify on LC at my fac. Pass more people through, let them go to low-level facilities that are currently short on trainees. If they wash, send more.
Set a level cap on NCEPT, at least for Round 1. Make it four levels instead of three though. Gives people a chance to jump and see higher traffic but more importantly forces better staffing at the mid-level facilities. Still allows people to go from a 4 to a 12 with only one stepping stone.
Do something to at least give a semblance of respecting location preference. Service Area, District, whatever. Might not be perfect but anything is better than the current "take it or leave it" system.
Allow Center trainees who haven't started training yet to swap facilities, no questions asked. Might not be "fair" to everyone but if it prevents transfers down the line it's a win. More of a thing for last year during the COVID pauses, but even now trainees at Zs don't start classes immediately, do they?