A new faucet would be nice. Of course that means cutting a 3 square foot hole in your tile....so lets look for a better solution! First, the Delta monitor series is a very nice valve, and eminently repairable. There are different versions, so we will need to clear that up. The first step is to get the handle off. A picture would help, but almost always there is a set screw as you describe. If it has been stripped, you will have to drill it out. Handles are readliy available, so don't be concerned if you have to bung up the handle to get the screw out.