Hi John, personally, I would leave it as is, as far as the major aspects, like arm or motor. Little tweaks may work out, but they are rather individual to the system being used. I think that a dedicated stand made of lightweight material, and very rigid construction would benefit the sound. Don't put it on top of your equipment rack. A Sound Organisation TT stand would be a very good choice.
Regarding tweaking in general, I always recommend looking at upgrade costs, before spending money on tweaking. Some tweaks can be pretty costly, and you may do better to move up to a different TT, by the time you get done with the cost of tweaking the one you have. So always keep in mind the cost of tweaking vs the cost of upgrading.
About the record clamp, some like the sound of a clamp and some don't. Also different clamps sound different. They are not cheap. Some cost more than your TT.
Tonearm damping is only effective if your arm is having resonance problems, and would be largely cartridge dependant. Overdamping can deaden the sound. You could try a little bit around the arm tube at 1/3 the distance from the pivot point. The Goldring cartridges I recommended would give a good match with your arm, and likely not cause any resonance problems for you.