More threads would help....
...but that would require remachining the clamp. I wouldn't go to that much trouble unless I were going to completely revamp the design.
I had thought about a design which is a good bit like a miniature caulking gun where the cylinder goes where the caulk tube would go. Obviously the geometry is all wrong but the concept might work.
I also thought of making a single chamber press using something like a specially shaped channel lock pliers.
My reading of history convinces me that most bad government results from too much government. Thomas Jefferson