I think this is fascinating--kudos to you for trying. I love the DB and always will, but who ever said instrument design had to stop? You can have a bass with no sound posts, and basses with sound posts, in the same universe, and nothing bad happens!
I'm a pretty fair jazz guitar player, and I think as Arnold said the interesting comparison is to the archtop guitar, which has a carved top and back and no soundpost. The archtop guitar was an attempt to get more volume by getting more of the string's energy into the top. It sort of worked but the original acoustic archtops were played with heavy strings and a pick. They had a tight, focused sound with lots of mids and none of those jangly acoustic flat-top overtones. Great sound for cutting through the mix in a band, or for making complex chords sound clear. Lousy for the old cowboy chords with lots of repeat notes. The envelope of the note is totally different on the archtop
I'm sure, absolutely sure, you could make a DB with no soundpost and an excellent pizz tone, but it would not sound like a traditional double bass. Might have real advantages. I doubt it'd sound good with a bow. I would think that you would want less of a neck angle, get the saddles closer to the top, because as mentioned yhou would have a different kind of bridge motion than the rocking motion. The Selmer/Macafferi guitars are really interesting to look at--they have a very interesting sound, very different from an acoustic flatop