Final Update (hopefully)
A few days after my last post, I went to complete the background check for the replacement. A few days after that I picked it up.
I checked it out and everything looked great. To offset the cost of the transfer fee and background check, they let me pick up to $65 of product from the online store for free. I chose a scope rail, and nothing else. So I installed the rail, bore zeroed the irons, and then bore zeroed a Burris Fastfire 3 (which I had lying around. Then the gun sat around in the safe until today.
I took it to the indoor 25 yard to get a working zero with Hornady 325gr FTX (because I have a few boxes lying around). Irons first, then the red dot. I wanted around 0.5" high on the irons, and exact zero on the red dot. I got close enough to be happy with it despite the red dot slipping on the rail initially. I didn't reinstall the Skinner sights I had, because I figured I might as well make the most of this red dot I have.
Here's where I left the irons. 4 shots, 25 yards.
Good enough for backup irons. The red dot gave similar results. I will have to fine tune it for my load at 100 yards.
Here's a poor shot of the new rifle.
So Henry did come through eventually. It wasn't simple or easy, but they did fulfill their guarantee of 100% satisfaction!