I can't quite visualise what you are clamping to what, but I'm guessing you want something which grips without needing a twisting action - so a conventional g-cramp would be no good.
Hold-down toggles are sold 'bare' for making jigs and so on - maybe some of those could be used?
Or else there is a sort of light weight cam-operated clamp favoured by guitar builders - maybe the cam action would be easier for you, and I guess you could fix two together side by side for extra rigidity. You can buy them under the 'Klemmsia' brand - eg here from Dieter Schmid Fine Tools
Paul Sellers did a recent video on how to make them.
Brian, your work is even more remarkable knowing that you have to hold the work with Mole grips.
Like the picture of the old Riley in your album. My dad had two Riley Monacos, a 29 and a 30, I believe. One was ash(thus relevant to this forum!) framed and fabric bodied.
Ok, I see what you mean now. I'd have thought the cam clamps would be ideal - they are available in a wide range of sizes, and the relatively large flat surfaces of the wooden parts should rest nicely on the bed of the scroll saw.
If you still get any slip, line the jaws with leather, or sandpaper.
I bought one of the AndyT wooden clamps from Axminster and it works well on ther scrollsaw when cutting small bits. It also ensures that the cut stays vertical, which is important. Being made of wood, it slides nicely on the table. I believe it would work well for you Brian.
Malcolm