If I had measured the setup before and after it wouldn't matter too much because I would just be 'dialling in' what I needed and then fine tuning from there. But if you're not doing that I would set the bridge first.
If the bridge plate is in a new position angle, the saddle height will have moved a little relative to the guitar neck. Get it back to where it was get it was before so that that variable is removed before adjusting the truss rod. In this case less string pull means you'll be loosening the two screws in the tremolo cavity. (You may have to do the adjust-retune dance a few times to get the bridge up-pull right where you want it, but that's OK). That alone may even fix some the buzz for you. Then you can happily dial in the correct amount of neck relief to fix what ever buzz is left over.
Again in this case a little less string pull on the neck means you'll need less tension on the truss rod. That means loosen the truss rod a little, i.e. turning towards the bass strings. You wont need much adjustment at all as you are only changing three strings. Maybe even no adjustment will be necessary.