Ken Timms sopranos are wonderful but I'd say mine sounds darker than my vintage Martin Style 0. That might be because the Timms is made out of Cuban Mahogany, so maybe the koa or Brazilian mahogany Timms sound more like vintage Martins. Nonetheless, it's one of the best choices out there.
I would put good money on Wunderkammer sopranos being the closest to vintage Martins from these smaller luthiers. I haven't played one or seen one in the flesh but every video with decent sound quality I've seen of them reminds me very much of a vintage Martin. Also, apparently they are astonishingly loud.
The obvious factory made choice would be Kiwaya, as has been mentioned already. My KTS-7 is incredibly close to the sound of my Martin, and the looks are basically identical bar the logo of course. Ohana and Flight have some vintage style models if you're on a budget.
Not really. Prices for Timms have gone down from the crazy days, at least for the mahogany sopranos. I paid about the same for both my Timms and Martin, and the Martin wasn't in the best shape. I'm pretty sure a pristine vintage Martin will cost you more.