www.garhauermarine.com
Thank you!Check the Garhauer cleat. Not as elegant as the Schaefer but it has a more positive engagement with the track. The Schaefer can rattle around a bit.
Midship Cleat MSC-2 fits 1-1/4" t-track | Garhauer
Stainless Steel Midship Cleat on a Car that fits 1-1/4" trackwww.garhauermarine.com
True. Hole in the horn and a flush allen head screw to fix it to the rail should do the job. Schaefer description also has this: "They will not fit earlier versions of T-Track or some competitors models."
Barton also does one at an attractive price: https://defender.com/en_us/barton-sliding-cleat

When you do get around to it: Flush screw(s) with a flange so they can't come loose and fall overboard. haha.View attachment 53967
We've got one on our boat and it fits just fine. On the other side is a ratty old aluminum thing that is barely big enough. Another Schaefer has been on my wish list for over a year, but hard to justify. - The $145 model you link is for 1" track. The 1.25" model is $155, still less than I've ever seen them. I do like that these are a solid casting, far less likely to come apart.
As little as it gets moved, something like you describe with a couple flush screws would be very nice. Eliminating that articulated pin should drive the cost down. If I were feeling ambitious, I'd make a pattern and get some cast.