The new Rega Planar 3

Sounds like a great rig you have going there and the motor kit and belt made a big difference IMHO. You might want to consider an arm spacer to get it to the right height. But other than that..........enjoy spinning some great recordings! You did well.

And as Williewonka suggests above you may really like the aftermarket platter, metal sub-platter and Michell Technoweight.

Viridian, agreed on the metal subplatter, I found the Isokinetik ISOSub GT 2 S sub platter to be a very good investment.

BTW - The actual brand of acrylic platter that worked for me was the SRM/TECH Acrylic Platter

This is one of the 1" or thicker  varieties available - with a thick rubber anti-vibration band around the outer edge.

When I was looking for a platter I came across several that were either 10mm or 12mm thick. Looked just  like the glass platter

Since I considered the mass of the glass platter to be crucial to performance, I believed that replacing the glass platter with an acrylic version of the same thickness would offer no benefit since it would be lighter.

Which type of platter did you try?

I have a RP6. Made several mods using Groovetracer. Dropped counterweight and subplatter. Subplatter made an immediate and amazing difference. Hugely improved bass and general musicality. If the subplatter on the Planar 3 is still some type of plastic, I would get the Groovetracer mod as soon as possible.

+1 on the GrooveTracer items.

So 
Subplatter
Rewire
Counterweight
Spacers(or Michell VTA adjuster?)

Looks like Rega P3 is just skeleton with no body!