Personally, I wouldn't hesitate to put a dab of epoxy putty or even silicone calk under the barrel near the forend tip before placing the barreled action in the stock and snugging the stock bolt.
Just be sure that it isn't applying too much upward pressure on the barrel. A couple pounds is plenty; use good judgement here.
Unless you're going to be pulling the stock out of kilter with hard sling tension in various shooting positions, it probably wont cause any issues, and will probably dampen vibration a little and help accuracy at least a bit; especially on a lighter, standard profile barrel such as yours.
Try it both ways, pop the epoxy plug out if it makes accuracy worse, and report your findings back here.
Heck, you could even slide an O-ring over the barrel into the channel or simply wrap the barrel with 87 layers of electrical tape at the forend tip to find out what works best before you mix up any epoxy...
But in the big picture, replacing your barrel with a good one will do more to help accuracy than any amount of fiddling with a mediocre one. ( Not implying that your barrel isn't a good one; just saying..)