I probably don't have your answer, but I've been wrestling with the same symptom for the last month or so. I also do not have a straight back, straight through stroke, being more of a "square to the arc" putter, as Utley describes it. That said, there isn't that much arc on six footers so we aren't too far off. For me, I believe it is mostly a loss of confidence in my stroke that has led to thinking about my stroke as I make it. This, for me, is a killer.
Here's what I'm working on, it seems to be helping, but I don't think I'm cured completely yet:
1 - Align with the eyes over the putter to make confirm line.
2 - Set up square to the putter blade, for me this seems to move my eyes back a couple of inches, and double check the alignment looks okay.
3 - Make a smooth and pretty short backswing, then think only of 'tossing' the ball toward the cup gently. You can no doubt do this thinking of either the back of your left or your right hand, but I think of a sort of underhanded right hand move toward the cup without really thinking any more about the 'stroke' than that.
This seems to be helping a lot, but I am planning to spend a good bit more time on the practice green in the next week or so working at it. Time on the practice green knocking in putts is probably the best cure for a confidence problem. And misses on both sides could be just that.