I know there's been discussions about creating a LTS ship for Jem'Hadar captains, and I fully expect that to happen eventually.
It occurs to me that there are other factions that don't have their own LTS ships -- Agents of Yesterday and Age of Discovery. I'd like to suggest a solution: add 2256- and 2270-style skins to the existing Chimera and Manticore classes.
I have no idea how difficult this would be to implement, but I can only imagine it's at least a little less work than creating entirely new ships. Then again, the Chimera and Manticore have many customizable parts, as well as custom animations. I really can't picture mixing and matching engine components from different eras, so I would expect there would have to be some restrictions to keep things manageable.