As I’ve discussed this with my users, we’ve reached the conclusion that this proposed solution will not work for us. The problem is that it still requires them to get an administrator to manually go into the URE panel before they get rights to the custom post types they’ve created. They’re still blocked from using the new CPT until the administrator does this, so it’s no real improvement over our current situation.
Ultimately what is needed is that if a role has the right to create new custom post types, it should have the right to immediately see any new CPTs created without the need for any intervention by an administrator.
Could there be a new setting of some kind that could be set to automatically grant access to new post custom types? With that, I as an administrator could say that I want new CPTs to automatically become accessible to the roles which I choose.