Essex camera and KEH will service the FG. This will run close to $100, when shipping is added in. This is in an age where you can buy a Nikon F3HP for ~$100.
My suggestion: use the FG. Look at the light seals under the back, and the mirror bumper. These are easy to fix yourself. If you are going to invest in a CLA on a camera, go for a top-notch one. The FG is a nice, light camera. Fun to use, with program mode. I'm saving my mint FG for my daughter to use when she wants an SLR.