It probably won't work very well to partially remove the clear. Strip or sand it off all the way and use a fine wet sand paper with water. You can do it in the sink. Say, light pressure 600 to 1000 to 1500 and then switch to hand rubbing with rubbing compound - OR- a chemical stripper that works (I forget what stripper I have used in the past). You could do a final polish with wax or swirl mark remover. Cotton cloth like old white Tee shirts are good for polishing. I get mine at the Goodwill Outlet store for this kind of work. I use Mothers aluminum polish a lot. Of course a buffing wheel works great!
I have also been known to use quadruple ought steel wool for jobs like this, plus a polish, with good results on brass, but some folks say not to. In fact, I think the last brass bridge I did was with steel wool.
Alembic brass parts are tough and you don't need to be afraid of doing this kind of stuff. On the bridge, you need to remove all polish and wax traces when done.
