If the band tightly 'binds' your barrel, it can cause accuracy problems as the barrel heats and expands.
It is desirable to have a 'paper thin' clearance between the barrel and the band.

If you create a shallow 'recess' around the stock, for the band to fit into when clamped, the 'recess' will retain the band and prevent it from shifting forward during sustained firing. The band should firmly clamp the wood.

(The barrel-band retention on original Krag rifles was a 'pin' through the stock and on carbines the band-spring).