The heads are the easiest thing to change (provided you have some around).
First: are you otherwise grouping well or is it an occasional fault? If it's only occasionally take what seems to be a good arrow and shoot that one repeatedly at a small aiming point (I use a 1" square piece of duct tape). It's not unknown that someone screwed up a batch of arrows and got the nocks crooked. It can also be something as simple as a nock isn't lined up well and the fletching is smacking the riser. Torquing the bow to one side on release will exagerate that problem as well.
Before you run out and buy new shafts I would recommend (if you don't have them) you get a selection of many weights of fieldpoints (Three Rivers sells a test assortment) and try them to see if you get a better flight with one weight. I don't think you're overspined with that arrow - but as I said I don't know aluminum shafts from Shine-ola.
I don't necessarily recommend 125 gr heads, but I will say I know guys who have used them for 40 or 50 years and have no problems killing game and scoring well at shoots. I have 35 years of happy times with them and the heaviest head I ever tried was 145 grains (and went back to 125gr). I think we have EFOC'd ourselves lately with excessive head weights. But then I only hunt thin-skinned 200-250# animals that don't have pointy teeth or claws.
I will toss this out: if you're already spinning the arrow for stability why make it extremely tip heavy? Penetration. I use a small head (1-1/8" wide RibTek 125gr, double-bevel) on a relatively heavy arrow (590 gr) and I taper the last 12" of my cedar shafts. They blow through a whitetail with the 52# to 60# of bows I use unless I center a rib going in; in which case they split the rib and still exit the far-side, though usually hang up on the fletch. And, IMHO, ain't nothing wrong with leaving a piece of shaft in a wound to keep it open and bleeding and not clogged with fat and lung tissue.