Cowabbi,
Be prepared for a bit of experimentation here...you might need to try different places to connect the capacitor and you also might need to increase it's value. Interference suppression is often more of an art than a science and what works for some things won't work for other things.
Try first across the 120VAC input where the mains lead is terminated in the record player.
Try from both sides of the 120V supply to the chassis of 1) the amplifier 2) the turntable.
Try from the shield of the pickup to the turntable chassis and then the amplifier chassis.
Try all these things with and without the earth connection to the turntable chassis.
Reverse the 120V plug in the inverter.
Try connecting the earth to each side of the 120VAC supply via the .01uF. Try connecting the pickup shield to earth via the capacitor.
If any of these start to look promising try increasing the value of capacitor; try .1uF.
Try also right across the 120V right at the inverter output socket.
If you're not getting anywhere there, get a mains suppression filter (not just a surge arrestor - that may not have any filtering) like used for computer gear( a 240V one is quite suitable), put 120V plugs on it, and connect between inverter and record player. You will probably have to earth the filter as the earth pin of the inverter socket will probably go to nothing.
Let us know how this lot goes [Linked Image]