Should I drill then retap the threads? Thanks!

Most seats are replaceable. With the stem out, look at the seat. If it has a square or hex opening, you can remove it and replace the seat with a new one.

I don't think I would try drilling. First, I wouldn't know the proper size to drill. Seats come in a large number of sizes, threads and shapes. The threads are usually a fine thread and are not the common machine thread. You will probably never find the proper tap. The seat threads have to make a water tight seat with the body of the faucet. The manual tap is usually a little over sized as compared with the tap used by the machinist. Even if you find the proper size tap you will probably have a leak through the threads.

Try removing the old seat with an easy out tool. The seat is brass and therefore a soft metal. Try tapping the easy out down into the seat with a hammer to give it a good bite in the seat. Then try to remove the seat. You may have to drill out the center of the seat to fit the easy out tool.
If that doesn't work you are probably have to replace the faucet.