Why not remove the race bonus alltogether and switch over to a class bonus completely? I think I would prefer this to adding just another set of bonuses which would increase the base attributes some more.
To address the OP:
I think that the real reason the designers got rid of the +1 from race, +1 from class stat bonuses is because they were intent on giving the human +1 to all stats, and the only way they could make that work alongside the other races was by giving them each a +2 to something.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.