I have a HQ16 (not a Sweet 16) that I bought used. It originally came with a table, then was converted to work on a frame, which is how I use it. I have a pcquilter that came with it, so the HQ16 is moved on the quilt based on a computerized pattern via the pcquilter, so I don't use the handles with it. (I could if I wanted to do free motion quilting.) I have fibromyalgia and arthritis, so even with the pcquilter doing all the quilting work for me, I do find that standing at the frame gets challenging at times. But since I have fibro and arthritis, there is no way that I can push a quilt around on a sit down machine.
May I suggest that you ask Handiquilter if the Sweet 16 can be converted for use on a frame?
I've never used a machine with a 9" throat. Even so, I don't recommend a 9" throat as I don't think it will make it that much easier to quilt, whether on a sit down table or on a frame.
Good luck!