7 star-ing characters is very important. Having characters 'unlocked' isn't enough I'm afraid. So you'll have to 7 star phoenix to get thrawn and palp up and running.
The SLKR route has been made very popular by Ahnaldt101. To be honest I'm not sure I'd recommend fast tracking a GL. It seems very difficult morale-wise.
I think getting core legendary teams up and running first, then focusing on a GL. However, if you 7 star Palp and Thrawn; they're both requirements for Sith Eternal.
Anyway, whatever you choose you'll need a 7 star Palp and I'm not sure how competitive you'll be in your fleet shard with a finalizer. I think being best in your fleet shard isn't your biggest priority. If it is, you'd have to fast track an executor or thrawn's ship and an interceptor maybe...