Something else to consider is bumping up to the next heavier string gage.

On my last string change on my strat, I put 9's on just to mix things up (I used to use 11's). I also lowered the action. I had significant string buzz of the sort where the strings would hit the frets a little as they vibrated.

I new I was eventually going to move to 10's, so I left it alone figuring I'd do a full setup on my next string change.

Well, I only had to make some minor tweaks. Just moving to the heavier gage strings eliminated the buzzing.

The reason is with a heavier guage string, there is more tension in the strings. More tension in the strings means they will won't move as much when they vibrate.