This may be the "magic bullet" you are looking for.
One of my friends has had a Plannar 3 now for about 10 years. It was never a "used" turntable, but in the first 4 years of owning it, he had moved so many times (college to home to California and then back), each time removing the plattter for transport, it was not in the cleanest of shapes. Around this time he had it set up at his folks house in NY and he complained to me over the phone all his records sounded noisy. He knew I was a more neurotic audiophile than him and therefore might have some ideas.
I drove down to visit from MA, mainly because we were forming a band with some other people, but while I was there he played me some records. Zappa's lumpy gravy sounded particularly awful, way too much crackle and distortion. I made a guess, based on nothing but intuition, that perhaps the heavily traveled glass platter was making a poor physical connection with the spindle because of the built up dust and grime. Boy did I hit the nail on the head! After restoring the connection distortion vanished, instruments had a specific space in the soundstage (like the CD version), and surface noise greatly diminished. He was extatic.
This is what we did, using cotton cloths:
1) removed and cleaned glass platter with rubbing alchohol
2) wiped the plastic spindle underneath the platter, as well as the belt and belt spindle, with a damp cloth, then again with a dry cloth, then reassembled the unit.
The most important part of it seemed to be the area where the glass platter touches the plastic spinde. In fact we went so far as to have one of us hold the plastic piece while the other person turned the glass platter slightly (at the end of the cleaning, just to sort of "grind" it in place).
There are of course other possible reasons a table can sound bad but your complaints sound uncannily similar.
Other reasons include (you probably thought of these already):
table not perfectly level
worn cartridge/poorly aligned cartridge
turntable not isolated from vibration- need spiked wall shelf or floor stand
poor phono preamp
PS he still uses the turntable to this day and is very happy with it. He has a vintage Target wall shelf (closest today is probably the Apollo wall shelf for $125) and believe it or not an Audio Technica 120e cartridge that just happens to mate very well with the P3 (get it from Garage-A-Records online for around $55!!!)
best of luck,