Changing your tire size has nothing to do with needing an alignment. What FastEddy is saying is that if you get the front suspension aligned with additional caster it will provide additional centering to the steering, which sounds like what you are looking for. A steering stabilizer won't help the steering return to center, it will just make the steering harder and slower to turn throughout the entire steering range - possibly a more dangerous setup if a quick emergency steering maneuver is necessary. You can safely add more caster to the suspension than what the factory specs state, and it won't create any abnormal wear on your tires - you may even notice a slight improvement in the handling due to the additional camber that is created when cornering (that's an old autocrossing alignment trick).

I'm not sure how much additional caster adjustment is available, but a good alignment shop should be able to work with you on it to get what you need.