It sounds like you're looking to get the most out of your current set up and are not looking for upgrade advice. With that in mind:
1) I'll second Viridian's suggestion to experiment w/ cheap/free tweaking and Phild's suggestion to get the disk doctor kit (which runs about 70 bucks). After cleaning, you should place the lps in new sleeves (AudioAdvisor sells pretty good sleeves--20$ for 50. Keep your stylus clean with the strike-strip on a book of matches--free! This is a hundred dollar investment that will get your lps _nearly_ as clean as an expensive VPI machine for a fraction of the cost.
2) Consider building some kind of isolation platform for your table. There are plenty of good ideas on the web.
3) Vinyl is a pain. Will your current tt be as quiet as your cdp after you've done the above? No. Will it sound different? Yes. Is the difference important and significant enought to justify the time, energy, and money you're sinking into analog playback? Have fun.