I use Irwin clamps too. My jig is different than yours (Lil' Jon) so I just let the "leg" of the clamp, brace against the table top.
For those that use strut as their jig length, there is a very simple solution. A short piece of 3/8 threaded rod, tall enough to be higher than your string, then a couple of nuts and washers with a couple of nylon washers to make a squeeze area for your string. The rod is supported with a springnut arrangement for your strut. You can also put a wingnut on top for ease if use. I'll check the DIY forum on AT for a pic.
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