Did you see the feat we have
Raising the Bar upthread? It works for bumping the racial maximum. I am pretty sure you did, but just in case.
I have removed the ASIs, but I did bump the ability score generation systems to include them. It gives a great starting point, IMO, maybe good enough players won't feel compelled to continually improve them.
The improved proficiency progression does pick up some of the slack, so helps IMO.
A flat +3 could certainly work. Our is currently +2 to +4 depending on level, so that would just use the average over the course of the game. Not a bad idea, really.