If it truly only moves backwards (towards the receiver) then the inletting is very tight, and the barrel contour is reversed from normal.
The forearm will need to be opened up to allow it to drop straight down, but I would avoid bedding the area right around the screws, as there's a good possibility the bedding will stick the screws in place. I would bed the entire length of the forearm, stopping shy of the screws, and also each end of the forearm. Putty around the screw area will keep the bedding from oozing into the threads, and sticking the screws.
As others have mentioned, I'd leave a gap on the rear of the forearm, the thickness of a business card.

I took off the forearm and relieved just a tad where it was rubbing in the non round part of the barrel near the receiver.  It now lifts off but the original bedding is tight but not uniform.  Next step is to remove some of the bedding material and to redo it.  The reason I could go backward to get to a part that was not as tight is that you have to really pull the barrel down with the front screw to get contact with the forearm so as I removed the front screw the binding allowed the barrel to raise slightly in the channel.  The gunsmith who built this barrel spent quite a bit of time machining the 8" or so closest to the receiver.  Took some pictures to try to post.  Tom

With that odd shape, the only direction the forearm can go is forward, towards the muzzle. Maybe the confusion I have is simply terminology. When you said it would only move backwards, I assumed you meant towards the action. From what I see the odd shape of the barrel would stop the forearm from moving back, and only allow it to move towards the muzzle.

The picture does not really show what happened when the barrel was seated in the forearm.  Believe it or not I had to slide the forearm toward the action an inch before it would come out until I relieved a tad of wood in the odd section of the barrel that was pinching the barrel and not allowing it to come off in the normal way.  I was beginning to think that the barrel did not have release agent when bedded years ago and was bonded!  I am not sure how little amount of wood I can take off the sides where the barrel has vertical edges so as not to show a line of bedding material but a slightly unsightly line is better than uneven pressure of the bedding material that will affect accuracy.  I am getting fairly good groups with a cold barrel but they open up as the barrel warms.