Patricia, your grandmother's machine was probably a 66, which looks just like a 99. Only the 99 is 3/4 of the size of a 66. The 66 was the best selling model of Singer machines from the 30's to the late 60's. As Leon states, there may be an issue in the 99 fitting into the standard sized treadle cabinet. I know nothing about that.
When I read your post, my first inclination (regarding the making the treadle work as a controller) was, "That won't work". Then, I questioned that thought.
Yes, of course, you can make it work. It depends on how much time you have, how much you want it and how much you are willing to spend. Making the treadle act as a controller is doable.
Finding a 3/4 sized treadle cabinet may not be easy. There may be adaptors, work arounds or other solutions to the problem. I just don't know.
bkay