LED turntable lamps/lights

Don't mod your turntable. It will negatively impact its value. 

Hi Mulveling -
I'm not sure about how to go about that on your Clearaudio table, but I had the same desire for a vintage SL1200 I had pretty heavily modded. I found a purveyor of DJ equipment in England on eBay that had what he called halo lighting for SL1200's. I installed it to great effect. I had already refit all other lights on the table with blue LED's and with the blue halo it was quite stunning in the dark! The installation involved removal of the plastic shroud under the platter and adhering the light array around the perimeter of the plinth under the platter. It was wired into the power on circuit but there is a downside; it introduced quite a noticeable bit of electrical noise that is audible at idle. There's probably a way to deal with that, but I set it aside right after I did it in favor of a MOFI Ultradeck with a Hana SL cartridge so lost motivation. 
Ken