Yes, I have rebuilt several CX-40's using the gold PCB and improved handle from Best Electronics. People who have hated the CX-40 for decades are impressed by the solid, clicky feel vs. the mushy feel of an original CX-40.
If I am reading the website correctly, Brad may be out of the improved joystick handles and may now use the OEM ones (not sure, I should ask him), but in your case, I'd replace the boot retaining ring to keep the stick together, then, if you feel the need to rebuild, look into the other options.
If you decide to rebuild it with the gold PCB, I'd replace the fire button spring while you're at it. It'll feel like a completely new controller and better than when it was new from Atari.