“Free floating” a barrel wasn’t always a “thing”, I’ve been told.
Close to 40 years ago, First rifle I bedded was a model 700 in 22-250 and the gunsmith where I worked instructed me to bed the full length of the stock
Shot great
Recently I had a lightweight rifle built and had a tough time getting it to shoot as well as I liked. Even re-barreled it twice with not any better luck. Barrel was floated
Decided to do something similar to what you did by jamming some cardboard between the barrel and channel. Helped a lot.
Took it back to the shop and they bedded the last 4” of the fore end and it solved the problem. Gunsmith said free floating a barrel is just something people want because they’ve been told its the only way to do it.
If it shoots, just bed it like that