Yeah, you are right. You don't want to be working in a hole.
Looks like the tube of the barrel is inlet. The next thing I would do is draw the outline on the stock, based on the barrel inlet, then cut the tang area to within 1/16 of where I thought it would end up based on the plan. I wouldn't cut the rest of the buttstock like that, though. I prefer to wait until I have the barrel and tang inlet, and the rod hole drilled, too, before I cut out the rest. With the barrel and rod hole in place, you have the foundation in place. The rest of the profile moves up or down in relation to that foundation.
I do cut off some of the excess in the buttstock area, just to reduce weight, but I like to leave 1/2" above and 1/2" below what the plan requires. That gives wiggle room.
On the rifle I'm working on now, I had a little thicker web than I wanted, and I went back and inlet the breach end of the barrel and tang in an extra 1/16". Of course that moved the buttstock down just a little. But I had enough wood in the buttstock that I could drop the barrel down like that without causing trouble. If the buttstock had been sawn out right on the final line, I wouldn't have been able to make that adjustment.
PS: Glad to hear that you are building this with him. Way to go!