I imagine there will be a good reason, but why not press the barrel back in to the front trunion, seat that assembly in the receiver, then apply the front rivets knowing that they'll flatten out against the barrel?
Worried about deforming the barrel? That it wouldn't be strong enough?
As an alternative, I have the following ready: I found a steel tool in my gradfather's shop (some kind of reamer) that has a shank just a smidge smaller than the barrel (.865 inch vs. .9 inch) I figure I'll set the trunion in the receiver, insert the rivets in both sides, set the assembly on a steel plate with rivet divets drilled in all three positions, and drive down the rivets from the top with a punch with a rounded divet in it. So all my force will be driving the rivets against the reamer shank which I can wiggle out when it's tight and then grind down the extra to accomodate the barrel.
Any problems? (and still curious, why not just drive rivets against the barrel?)