I shoot wood, so I'm only at 15% FOC, so take this with a grain of salt.
You should be able to get straight flight as if you are shooting fletched shafts. Unless you are shooting with a machine, or you are a world famous trick shooter than can robin hood 4 arrows in a row, I would tune to arrow flight and not point of impact. To me, there are just too many factors that could contribute to you shooting left or right of your target.
If it were me, I would either build the side plate out and see if that helps at all. If it does, than you know your shafts are too week. If nothing conclusive comes from building out the side plate, then sacrifice one arrow and start cutting it down. You should be able to get it to fly straight (to your eye) at 20 yards, in my opinion.(at least I can, but I've never played with UEFOC carbon arrows)
P.S. are you tuning with field points or broadheads? I would tune with field points first, then tune your broadheads so you have a baseline to work from.