I had a Ruger No.1 that I thought improved somewhat by putting a bedding pad at very tip of the forearm - I think that created a bit of "up" pressure on the barrel. Several factory Winchester Model 70's seem to have been done that way.
I do not recall anything except grief from a rifle that the fore-arm contacted the side of the barrel in the odd place. Opposite that, probably my most accurate 243 Win was a Remington 788 that I solidly and fully epoxy bedded from rear receiver tip all the way to the forearm tip - so that barrel was in full contact for it's entire length within the forearm - it shot very well - and continues to shoot well with a take off replacement barrel in 308 Win. I can not get the thinnest feeler gauge - .0015" to go in between barrel and that epoxy bedding - anywhere along the fore arm.
From that, I believe that tentative contact - sometime there, sometimes not - is about the worst to have. Could be caused by inletting not cut straight to match the barrel and receiver. Could be because the action screws or recoil contact is not solid and the action and barrel can move and not return exactly to battery from shot to shot. Could be because the forearm has altered its shape from heat, cold or moisture change.
I suspect it is mostly about letting the barrel have the same vibrations - the same "shivers" - as a bullet coming up the bore - so that the muzzle is in same exact place as the bullet exits - the muzzle apparently "whips" or "oscillates" as the bullet is coming along the bore - so most accuracy is when it is exiting exact same portion of the oscillation, each time. Where, and how tightly, it is pressed on by the fore arm will change that pattern, I think.
OP - I have worked on a friend's Ruger 77 with wood stock and now have my own Hawkeye - digging for spec's, I was shocked to read that Ruger calls for 90 to 95 inch pounds torque on that front action screw - that is some serious torque!! Might be a place to start checking - find the Ruger specs for the action screws and hit those numbers, in the tightening sequence of the three action screws that they call for. For reference, that front one is about double or triple the torque value found for many other rifle action screws.