I always target Biggs right away.
There is more than just a bug with his protection being over regenerated from target lock. Occasionally he will regenerate protection for no reason whatsoever. No consular, No Rex, no target locks up on my team, no commander ability used...
My guess is that the reinforcement "target lock" bug is really just a reinforcement bug, and that he regenerates protection whenever one of your reinforcements takes a turn.
So my strategy in taking him down (if I can manage it) is to use my full Republic Fleet (Plo Koon, Fives, Consular, Clone Sergeant, & Rex starting; Ahsoka, Boba Fett & GeoSol as backups, Mace lead) because I can mitigate damage like mad in between consular, mace, plo and Rex (especially Rex, he's almost not worth running if you don't have a full Mace led Republic fleet, he restores tm and protection every turn in that setup), which will usually keep me from needing to reinforce, which means that Biggs doesn't bug out, and I can wear him down after a few minutes even in a target locking vader group. Vader really does a number on that damage mitigation though. Any group without Biggs or Biggs/Vader is easy. (Which means mine is easy I am sure)