Bigsby comes stock with the gretsch electromatic baritone. Is bigsby a possibility on the viking baritone? If so, which type of bigsby and would it work with a vibramate? What would be the best bridge for such a setup?
As long as you have the stopbar version and not the floating tailpiece I think it should be pretty easy to drop in a Vibramate. Either the new V7-335 (check the dimensions; email Vibramate if you're not sure) or the standard Vibramate with a B-5 should work.

As for the bridge, I like the Resomax with the graphite saddles, or a decent roller bridge. Schaller makes one.