Any liquid cleaner is a GREAT way to attract more dust and dirt. Don't do it. If anything it should be cleaned properly and then regreased with ceramic grease. It really doesn't sound like a stuck gear being the problem.
And actually, the laser moves from the outside to the inside to read the disc at boot. It'll move to the outer edge to verify the security "barcode" at one point and then back to reading the data to boot up the game.
This is also a bit confusing:
So the game will play and freeze at a loading screen randomly? Are the discs scratched? Is the ribbon from the controller board to the motherboard secure and undamaged?...play the game as it properly should for a little while but after a little while it will often freeze at a loading screen and then I have to repeat the process all over again.
I'd also try cleaning the lens with a Q-tip and rubbing alcohol. Dip the Q-Tip into some rubbing alcohol, tap the stick portion a bit to remove any drops that may end up where you don't want them and gently rub the lens. It doesn't need much pressure and you shouldn't cause it to dip inwards at all if possible.
Give it 10 minutes or so to dry and try again. If it doesn't work it might need a new laser. I've got one here that works great as well as several modchips. Saturns are fairly resilient creatures.