Test1328: I have been "shooting" pre-64 Model 70 Winchester Standard Rifles for 50+ years now.
I have shot these Rifles in calibers 30/06, 257 Roberts, 300 Winchester Magnum, 300 H&H Magnum, 270 Winchester and a bit of 264 Winchester Magnum.
I was always able to attain accuracy just a little better (1.00" to 1.50" five shot groups at 100 yards - I no longer shoot five shot groups in the larger Hunting calibers unless doing initial load testing!) than what you are getting.
I always checked adjusted and then shot with that forend screw, snug, plus!
Never had to "fiddle" with that screw to attain "good enough accuracy" that I recall.
I do have three what I consider semi-custom and full custom pre-64 Modle 70's and I have added among other things hex-head action screws to them - I do torque them to known and repeatable inch/pound readings - they don't vary much from Rifle to Rifle.
I wish I had done more "experimenting in your regard but I just haven't ever had the need to do so.
I do have one friend who once he decided to dedicate a pre-64 Model 70 to Hunting only he left the forend screw out completely and his Rifle shot very well (30/06).
Good luck.
Hold into the wind
VarmintGuy