There are several approaches you can take. You can use an existing WPS that addresses the use of GTAW and filler metal additive or you can write a WPS that is specific to the repair that describes any processing steps such as grinding the existing weld to sound metal, the shape of the excavation, etc.

As for the repair made without the addition of filler metal, I suppose you could qualify the technique by replicating it and performing the mechanical testing required to demonstrate the mechanical properties are obtainable.

Best regard - Al

Al gave you solid advice on your question and after you get to the bottom of that, you can work on fixing the process to eliminate rework and make yourself look real good at the new gig. That could entail qualifying a new procedure completely, but if you have to do it to fix your problem, it could be worth looking into qualifying a new more consistent process entirely. You could go with Tip Tig root - GMAW fill/cap, GTAW root - GMAW/Fill Cap to raise the consistency of solid welds. Current process times with rework would have to go up against new process times hopefully without rework, but I've seen some tip tiggers deposit and travel as good or better then a mig welder. It Could also be as simple as changing the parameters within your current process to produce a better more consistent root pass along with training, all the while staying within your current procedures essential variables of course. Are you able to roll these welds out on a turntable? For time being, my 2 cents would be to make them do the repairs with filler using existing wps (if I read that right in that you have one) to stay code compliant until you nail down root cause. Making it a pain in the rear for them might make them try harder and think about how to put in a good weld the first time.  Best of luck to ya in your new gig.

Kix