I'm going to try to break it down by company for clarity (I have some time on my hands, apparently):
Bluetop (from my emailing with them): (Me: what's replaced in a rebuild?) The seals, bearings, and the ball bearings that we size for the worm and piston. The worm, piston, shaft all are used again. There is typically really no wear on those parts at all unless someone has over adjusted the gearbox and driven it for too long. (Me: What if there is wear?): Yes that would get fixed too if that was worn.
I have one more email to them asking about the channels being an issue on center, per Pete's concern above. Edit: Here is their response: "Yes it does. (I asked if their reman resolves this on center issue with the channel) Thats where the oversized ball bearings fit the groove perfectly. There really is never any wear in that spot more so just two surfaces that were not matched up correctly at factory when new."
From searching on forums, I have found one complaint of a new box getting sloppy, which BT rectified. They don't carry a box for E-series off the shelf, so I would have to send mine in, which they say is a one-day turnaround. That complicates things for me, but they carry boxes for most Ford trucks. They seem to be the go-to now. There was even a group buy on the Ford truck forum.
Ford Motorcraft (info I've found on forums, so may not be true): New sector shaft, but bearings are the same (lower tolerances). I haven't seen anyone complain about them on any forums. Most complaints are about Cardone and Lares remans. Edit: did find a complaint of one leaking after a while, think it was 60k miles. Edit: One person said they had a leak in a redhead and got a Ford instead and prefered the tightness of the Redhead despite the leak.
Redhead (also forum research): Some people "swear by them." I found some complaints, (don't have links) and there is an opinion among some that quality is slipping, hence the move to Bluetop. Edit: Found evidence of a leaking box that had to be replaced with Ford reman, but that the person liked the RH better due to better steering feel. Here's a link to the thread on sportsmobile where people have issues. It's funny, people still prefer the RH over the Ford reman in terms of steering response.
Lares: Supposedly new. Can't find much about them except people having issues with their remans. But is this new box really new like RockAuto says it is? Some folks on the forum say there is no such thing as a new box, but am I to believe them?