A lot of people here have used the LED fluorescent replacement tubes. I'm sure you can search and find numerous threads on them.
We used the Ming tubes available from several retailers because they don't use the existing socket for electrical connection; they connect via a wire that comes out of the side of the tube. I was concerned that the sockets in my fixture were possibly contributing to the problem and I didn't want to use them. The cost of two LED tubes was less than the replacement cost of the fixture; IMHO there's no reason to do anything other than use LEDs in your situation.
