I use an oversize square grip which helps me to keep my hands , and putter face perpendicular to my chosen target line. I also have both my thumbs on top of my grip per your question in your last post. My putter head is also on the heavy side at 600 grams, which I am sure helps with the extra weight of the oversized grip.

On another note. Although I think it is not legal, I put this same type of square oversized grip on one of my drivers. I was just horsing around in my grand son's garage when I did this. When I took it the range I was surprised how well the driver worked for me. Yes, I did have to add weight to the club head to balance it out to get a good feel. Just tinkering around. GJS