FWIW - My two cents - I would make the nut in a trapazoid shape. The longer parallel side would be at the top. I would groove that side to fit close to the barrel.

The angled sides would be as long as necessary or desired. A cross hole through the angled sides would accomodate a cross-pin, notched at the ends, to link with the band.

The short parallel side, at the bottom of this rig, would be drilled and tapped for desired screw or de-tachable swivel stud.

I do not see merit in keeping the barrel-band 'sides' parallel. If they are drawn inward, less wood will need to be removed.