Almost looks like the tool was made for another purpose. Usually the barrel vice is mounted on a heavy bench and the action is turned with some type of wrench. You may make square OD and round inside bore bushings to fit or possibly just use bent soft aluminum or brass sheet metal Vs to fit?
There is always a different way to skin a cat, so you will be able to use it, may take a little more thinking to make it work.
Speerchucker in this Practical Machinist thread uses a shop built vice bolted to his milling machine. Note him tightening those 3/4 nuts!
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