I would not put a Singer 15 on a frame. It's not the height, it's the length that is going to be your problem.
BTW - "mid arm" is usually 18" or less.
The Singer 15 is rather short needle to pillar, so when you get the quilt loaded, you are going to find that you have very little room to move forward and backwards. An extra inch or two is a HUGE difference, way more than people think it will be.