Riveting is actually one of the easiest parts of doing the build. Order a couple sets of rivets, make the bolt cutter tools, and give it a shot. If you screw one or two rivets up, do it again. By the first couple you'll have it down.
If the barrel is populated, pinned, and headspaced to the trunnion, most of the annoying shit is already done. A press isn't even needed to install the barrel, just tap the barrel into the trunnion with a good set of brass pieces to act as non-marring buffers against the muzzle, and use the carrier to support the trunnion. You can support the tail end of the carrier with a brass collar threaded to a short length of pipe.
That being said if you can spare the few hundred bucks and just want it done, and can wait a few months, it's certainly the easiest, but the satisfaction of having done it yourself won't be there.