You’re asking for too many things in your SLKR counter, something is going to have to give.
I personally think you should go the Jedi route. 5 out of these 6 make extremely reliable counters to both SLKR and ALL forms of GLRey: JKR, JKL, Bastilla, HY, Old Ben, General Skywalker. These characters are also good enough to take out any DRDM or 501st team.
They also fit your requirement of remaining versatile outside of an SLKR counter.
If you watched YouTube videos, Xaereth Prevails has I believe FOUR videos on JKL/Jedi counters, along with how to move them around if you don’t see GLs in your GAC. They are indispensable, you’ll really want to learn these strategies if you want versatile counters to GLs.
I strongly recommend gearing those Jedi for those reasons if you’re looking for answers to GLs