just checked my nut and i belive its cut properly, the slots are cut at a light angle according to the strings and it's the factory nut from gibson, as for the bridge it's a wrap around so it can't really be that. i will try doing that self locking thing when i go to restring.
Your tuning stability problem shows up on which strings? I assume it's some strings more than others.
Even if the nut slot is cut at a useful outward angle, there are still 2 other things about how it's cut that can be the problem:
1. Is the slot cut at a downward angle towards the tuners? It should be. This matters more on Gibson's due to the angle at which Gibson headstocks lean back.
2. Is the nut slots clear of any debris or rough spots left over from when it was cut. Just a little rough spot or piece of nut-trash in the slot can cause string binding.