With copper shielding in place you should be able to press the bridge forward and leave an impression on the copper showing you exactly where the pickup is hitting the in the cavity, then you can work out the best way to tackle it without hurting your finish. I think with mine it was mainly in the corners, particularly on the bass side. If you are lucky you may be able to get away with just shaving a bit from the corners and give the leading face a slight undercut, depending on your pickup and how well the rout was originally cut.
Post some pics of the cavity if you can as it may help work out the best approach.