Bedding and Accuracy.

[muffett.2008]

The forend stud and spring become redundant once the nosecap is removed, the spring bears on the bottom of the nosecap, applying upward pressure to keep the barrel centred in the nosecap.
If correct tension has been maintained on the last inch of the forewood, there would be minimal change in POI, it will rise slightly.
Removal of the inner band, should have little effect on a correctly centred barrel, however, if the barrel was previously bearing against the band, then that's another ball game.
Contact from the inner band will dampen and change vibration, as will any contact along the barrel from the knox to the last inch of muzzle, between these points the barrel should be clear of any contact if correctly setup.

As to the split groups, you probably have insufficient down pressure at the nosecap. The load should be between 4 to 7 lbs, the nosecap should. slide on without the need to force it, if it requires force than the inch bearing surface needs to be adjusted.
This is where the target fraternity would place cork packing in the top handguard to maintain downward pressure as the barrel flexed as it heated up.