I discovered that having the fingerloop around the middle or ring finger, and having the fingerloop on the inside of your hand, with the retention cord hanging down over your index finger while gripping the release cord with your thumb and index, does the same thing as the thumb grip, but in a much better way (for me)
I advice to experiment with as much different grips as possible, it can really make a complete difference in accuracy. Previously I have always slung with the fingerloop on my middle or index and have the loop on the ouside, like Luis does in this gif
https://gfycat.com/grouchyseveralleafhopperBut having the loop on the inside of your hand instead, totally slings different and works much better with my slings.
I think if you've been slinging for a long time but your accuracy is still bad, try different grips. It can make a world of difference. Sometimes we get stuck in old habits