You could save a lot of time and money by using an existing cartridge. For one thing, somebody already engineered and maybe manufactures casings for it. And you'd avoid the NFA hassles if you picked a cartridge that somebody already spent the money on to get a Sporting Use Exemption for the DD.
M.K. "Ken" Owen, River City Rifle Company, Moscow, Tennessee, is one of the last remaining custom builders of dangerous game double rifles in the US, and he has built 4-bores in the past. In rifles, a 'bore' is not a fixed measurement. It varies with the exact density of the lead used when slugging the barrel. A typical 4-bore is just a smidge over a 1.0 caliber, so it should be no problem to tweak the alloy to reduce the diameter to 0.935". And if Mr. Owen does not machine them himself (which I'm pretty sure he does), he at least can put you in touch with whoever makes his casings for him.
And there are enough 4-bores in existence that I would think somebody must have ponied up for the SUE, which you should be able to piggy-back off, although that might mean having to scale up to a full 1-inch diameter. I'm sure Mr. Owen also would know the particulars on that account.
If that doesn't work for you, check the BATF's list of obsolete cartridges. That might have something that can, like the 1.0-cal or .80-cal Gatling cartridges.
