I use one on right for knocking the weld down and then i use the one on left to put a smooth polish to finish it off. I think a cut off wheel is gonna be about your best bet from the sound of it. Just have to be careful and keep cutting then looking then cutting then looking making sure you are exactly where you need to be. If you cut a little bit in to the piece all you have to do is put a spot of weld back in it and then smooth it off with grinder on the left. Also depending on where you are working with the frame at a porta band is an awesome machine as well for cutting things off.
-Justin