There are those who insist a certain type of turntable works better for CD-4 than others but it is all talk.
It doesn't really matter what type the turntable is as long as it allows the cartridge to track well so it can retrieve the ultra sonic carriers consistantly. It can be a linear tracking, direct drive, radial tracking, belt drive (what I use - a BIC 980), or any combination as long as the tracking requirements are met. Heck, Panasonic even used BSR turntables successfully in their all-in-one CD-4 systems.
What is more important is to be sure the wiring is low capacitance (100pF or less) between the cartridge and demodulator so the ultra sonic carrier signals are not attenuated.
So, I would just take your best turntable for CD-4 (The SL-5) and put a good CD-4 cartridge in it and use that. Tweaking comes after installation.
Some of the best CD-4 cartridges of the day were:
Panasonic EPC-450C II, EPC-451C, EPC-460C (These are semi-conductor cartridges and require a demodulator which can supply the bias voltage necessary for the cartridge to function. All Technics and Panasonic demodulators had this capability).
Pickering XUV-4500Q
Empire 4000D I, II, and III.
Audio Technica AT15Sa and AT20SLa (although any of the AT quad cartridges work well)
Empire 440D
Shure M24H
A modern day magnetic with great CD-4 capability is the Audio Technica AT440MLa which has a line-contact stylus.
And yes, a Shibata type stylus is almost mandatory for successful retrieval of the carriers although some cartridges with ellipticals claim capability (grados, e.g.)
Doug