I actually just went through this frustrating exercise over the weekend! Here's what worked for me.
I run an Atlas bipod with the legs kicked forward a notch and extended enough that I can clear the grip from the table and not much more. I don't preload the bipod, and I use a tall sandbag under the stock that I "build" up a bit. I then settle in with the crosshairs under the target, and press my face down into the stock and smoosh the sandbag until I'm on.
FWIW, I also started shooting at squares a few years back after shooting at circles for years, and I did notice a pretty big difference in how repeatably I could shoot groups. Not sure what you use for targets, but I just draw 1/2" x 1/2" squares on grid paper, and I aim at the bottom left corner. Seems to have improved my shooting some. Your mileage might vary.