I use the standard reverse overlap grip. I'll have to give the index finger a try.

I started putting a lot better when I went to more of a "feel" stroke. I practice putting by putting something down, e.g. an extra ball, a coke, my glove, at a spot on the green, 3, 6, 9 feet away and putt three balls. Not going back from the 3 to the 6, etc. until I've made the three. I got into the habit of taking the three balls at the cup and nonchalantly putting them back to my marker. I found that I was more accurate with the nonchalant stroke than I was with the stroke lining up, thinking about the stroke, having all kinds of thoughts, etc. So now I basically line up the name on the ball with my line, eyeball the putt for distance, uphill or downhill, grain, etc. and try to get a feel for what the putt will do. Then I line myself up to my target, relax, think only of keeping my head steady and let it go. I can usually get the long ones within the 3 foot circle and sink my share of short ones.

This "feel" technique has helped me a ton.