At this point I don't think optics, or possibly even the courts will allow for the NCAA to tighten the rules around the transfer portal in any way that will restrict the players ability to transfer. The paste is already out of the tube on that one.
So why then can't the NCAA put some restrictions around the schools with regards to accepting players from the transfer portal? Each team gets 85 scholarships, so then limit the number of transfers that a school can accept to 9 players a calendar year (roughly 10% of the scholarship allotment). The players can still enter the portal all they want, but the schools will have to be a bit more selective in who they pursue. I would also consider putting a restriction within the 9 allowable transfers that no more than 3 or 4 players can come from one particular school during the calendar year as well. That could put a limit on pulling something like what Lincoln Riley did when he tried to take half of his Oklahoma team with him to USC.
With regards to coaching changes and the 30 day window that comes with that situation....I think a solution would be to only let those players that have completed 2 seasons with the school be eligible for the 30 day transfer window. The older guys with less eligibility have more exposure during a coaching change due to the system of the new coach not fitting with the skill sets of some of those players....so let them finish out their career at a place that is more suited with their skill set.