Hyper G Round is about the same or even a bit stiffer than regular HG. 1.20 HGR is still significantly stiffer than HGS 1.25, You have to go to 1.15 to be in the same stiffness ballpark as HGS 1.25. Then you have gone down 3-4 grams in weight, losing 6-8 SW points, which means adding weight or having the frame play completely different.
There are softer round 1.25’ish polys with similar stiffness to HGS like YPTP 1.25 or Cream 1.28. Maybe try one of those? FYI, tension maintenance is much better with the YPTP but it costs a lot more.
Or, you can just try HGR 1.25 and drop the tension a lot, which is probably where I would start.