Any clamp that holds a 3/8th inch rod will work. I've made a few suggestions below.
Try positioning your Machine so the mounted beater is perpendicular to your stick. This gives you the most surface area to hit, and increases your accuracy.
The entire Machine can be hidden behind a music stand, or perhaps a cymbal, all you need to see is the beater.
You can use most anything to play your triangle.
In the Broadway Production of The Addams Family, I had a solo triangle cue that I played while sitting in a chair, pretending to read a book.
I was 6’ away from the Machine and used a long piece of dowel to hit the mounted beater :)