I've noticed that many times barrels will be touching the forearm at some point or like you said, be favoring one side of the barrel channel entirely. I don't know if this is from the forearm not being truly straight or from the way the receiver is sitting in the stock. Either way, I've successfully fixed it a few times now.
When you bed the rifle action to the stock, make sure you wrap tape around the barrel about 4-5 times near the end of the forearm. I usually do around 5 wraps about 1/2 inch from the end of the forearm. That way when you bed it, the bedding compound will harden in the correct way to have the barrel centered.
In fact, my favored way to bed is that the only rifle parts that are actually touching the stock is the tape near the end of the forearm and the last 1/8th inch of receiver tang in the back. Everything else is bedding compound.
You take it all apart, take the tape off, clean up the bedding spillage... When all is said and done, the barrel is true to the forearm. Even if you physically push it one side or the other, the barrel always comes back to center... not touching the stock on either side or beneath.
That process should help most of the time. Unless the stock is really curved like a banana.