You may want to do look around for a better data connector solution. Those RJ-45 plugs and jacks don't stand up to a huge amount of cycles... especially the tabs on the plugs. They snap off like stale cookies.
You also have to go through the hassle of aligning the rotating portion
exactly dead center, and/or find some way to compensate for shifting in the rotating mechanism and contraction/expansion of the wood. Here's a
discussion about different electrical rotators out there.
Some of those rotaters are insanely expensive. I like how compact the Mercotac is for instance, but when I spotted prices in the $150 range, I decided anything more than a simple RJ-45 jack is going to be out of reach. Since I never intend on building a rotating CP, here's my idea. Feel free to use it. (I doubt anyone ever will, but whatever.)
Let's say you use two rotating
Lazy Susan bearing. That leaves a huge center hole to work with. Down this center, you run a fixed plastic pipe. I would prefer PVC but it's kind of bendy. Let's assume PVC for the rest of this. Down this PVC, slide down alternating metal and plastic PVC collars. After you slide down a metal ring, drill a small hole through the pipe, run a wire down the pipe and up through the hole, then solder it to the metal ring. Then slide the PVC collar over this hole and repeat. You can easily get 8 connectors for two USB connections or one USB and 5+, 12+ and grounds or whatever else you need. Install down the center.
On the rotating CP itself, install some kind of horizontal brace off center, such as another pipe, mounted with an inch or two of the fixed center pipe. Depending on what metal collars you chose, you can do brushings or other types of connections.
For a brushings style. Off of the brace attach strips of metal to act as brushings that align with the metal collars on the center pipe. Two screws in the metal brush should prevent the brush from twisting or the plastic collar can act as a track. Adjust until brushings make contact. Run wire from brush to wherever on CP.
Another idea I had was to loop a piece of small solid core wire around the metal portion of the collar. This would especially work if there was already a groove in the metal or if the plastic collars were larger than the metal creating a groove. Apply some conductive grease to lubricate and prevent oxidation. Binding might be an issue, so looping a spring to make contact instead of a wire might prevent binding and have the added benefit of being self adjusting as the the whole assembly settles out of whack.
Both of the above have the drawback of requiring maintainence as the metal brushes/wire/spring wears down, requiring replacement. Buying a huge box of springs or strips of metal and premaking them all at the same time should ease replacement woes.
A more complex idea would be to have a spring loaded arm with a bearing on the contact point. I haven't worked out how to get that idea viable though.