Being that its the cross bolts against the barrel channels that indexes the tube front to back, sounds like to really solve the problem, facing the front of the upper receiver barrel extension face would the final solution.
Hence you would face the front of the barrel socket back, which will allow the barrel nut and it two grooves to be farther back towards the receiver when the barrel nut is tightened, so when the cross bolts are installed (no longer a drop through fit, but a tight wedge type fit), they are wedge tight against the front of the groove channels forcing the tube tight to the front of the receiver, to prevent the tube to be able to slip forward in the first place.
As for the distance that the front barrel socket edge needs to be faced back, install the bolts against a tightened barrel nut, pull the float tube forward so the bolts are tight against the front of the nut groove channels, measure the gap between the back of the tube and the front of the receiver, then add in about .010" to that number. Now with the front of upper barrel socket set back that amount, the barrel nut tighted, the cross bolts will have a .010" wedge fit when the are installed, with this wedge also the tube to the front of the receiver as well.