The rod along the left side of our miniblinds turns a shaft spanning the length of the housing which pulls-and-releases three pairs of cords tilting the blades, with one roller for each pair. The cords loop over, pass under, and are secured to a tab on the roller with metal ferrules, thusly:
One day, the middle section of all the blades on one miniblind stopped tilting, prompting this discovery:
The correct solution is, of course, to replace the entire miniblind, but our 1955 window frames don’t match up well with contemporary miniblind hardware and I was unwilling to reinvent that particular wheel for this occasion.
So I laid the cords in place, put the broken tab atop them, and held the mess together with a strip of the obligatory Kapton tape:
Easing some epoxy under the tab and soaking the cords atop the tape held everything together in approximately the original layout:
Two days after I reinstalled the miniblind, a second roller broke and was restored by a similar treatment. While I had the thing on the bench clamped in the bench vise, I preemptively slobbered epoxy on the intact roller in the hope of reinforcing it.
So far, so good!
The Smell of Molten Projects in the Morning 
Tom Lipton?
Hadda look the man up.
Obviously far beyond my skills & equipment!
I guess I figured you already knew about him and from your copper vice jaws. Good, you have a new resource, make sure you check out his books as well.