I think that set up for clamping looks great in a steam punk sort of Jules Verne way
but is actually pants
I think the reasons have already been spelled out. Just take off the top section and the ironwork. Use good ol' rubber wraps it will give much more even pressure.
If you do want to use the jig, as is, use wedges with a very shallow angle pushed in from alternate sides with very little gap between 'em.
Oooooh just had another idea!
Put a layer of rubber tube/strap wha'ever between boo and top former then apply pressure to the top former by putting wedges under the bolts that go through the very top of the iron straps !? Yes?... No? ... er maybe. At least it's quick and simple and it uses the jig in it's full glory... mind I thonk some domed brass nails tapped in along the bottom would add to the look
Prob' best idea is to sit and have a beer and think
Del
(PS. Not my area of expertise either, so maybe I'll join you for that beer
)