In the real world, this greater than infinity distance doesn't exist - but if it did, it would be in focus!!
I've been working on acquiring a full stable of MF Nikon lenses, sending them in for cleaning as necessary, and at one point several years ago one came back focusing past infinity. I called the repair shop (one of the most respected, most recommended Nikon repair facilities) and talked with the technician about it. He said that at a Nikon workshop they'd been told that some of the AF cameras won't pick up focus at infinity in manual focus mode and give the green light unless you focus past infinity and come back from there, and they'd been told to make the lenses go past to solve that issue.
I estimate focus a lot (the particular lens was a 28mm), so I sent the lens back, and he set it right, warning me that from now on I should tell them if I wanted to keep the lens as it had originally been made.
People on other boards start arguing with me about whether this is necessary or not (infinity should be pretty easy to find without the dot, shouldn't it?), so don't start in on me--I'm just repeating what the technician told me. I can believe it--some camera users are pretty dumb (for instance, I note that today on another forum someone's asking what the proper AF selection points woud be for landscapes, since his camera isn't giving him sharp landscapes).
Anyway, I wonder if your lens may have had a CLA in the last few years, and that might be what causes the problem.
The other cause would be if your camera's mirror needs adjustment. This tends to show up on wide angle lenses more than teles, as an infinity that's slightly off, one way or another, and seems to be a very common problem with older cameras. I've had this on two OM1s, a Hasselblad, and a couple of Nikons. You need to eliminate this possibility before you start in "fixing" lenses that aren't broken.
using the end stop on the focus ring for fitting or removing lens is not a wonderful idea
The OP spoke of Nikon, and I've had a fair amount of experience working on Hasselblads, which are supposedly divinely made. And from what I have been able to tell, "infinity" is all over the place on Hass'. I haven't been able to pin down any kind of "infinity" on any of them yet. So far, a well-adjusted Crown Graphic and Kalart has them all beat.
I had, and still have, this lens (50/1.4 ai) for so many years. A couple of years ago it started to stop short of infinity. I took it apart with the help of an online guide and moved it a little and now it's spot on. If I remember right the adjustment done by loosening a small screw and moving a brass disk that lives beneath the front element a little bit and checking until you get infinity right.