Welcome to the forum.
VSL has never offered articulation sets for Logic, even when the number of dimensions was three or less.
Do a search on "Audiogrocery XDAW." This is a third party program designed to accommodate far more than three keyswitches. Its developer, Ivan, is very responsive to users' questions. There is, however, a learning curve.
XDAW allows three different ways to create articulation sets. It can be used as a simple builder of three-switch Art sets, in which case you just save the set in Logic's correct folder. You could build the very same thing in Logic, but XDAW has features to expedite the build. However, because of the very issue you mention, a straight-forward Logic Art set, no matter where or how it was built, only drives three keyswitches -- hence no Synchron String Pro / Elite.
The last two ways include automation and the use of Scripter. Either of these two is required for more than three keyswitches. (You don't have to know how to write scripts.)
I rebuild my templates frequently. Sifting Synchron Pro / Elite Strings into no more than three dimensions is a challenge, especially if you want to preserve all the options. It's a great way to learn the library and the Synchron Player. But it does take time.
If you pursue XDAW, ask Ivan if he has any pre-made Synchron files.