It's been done a few times, mostly by people in Japan.
The first question is why. You'll never get a carb setup to work as well as a good fuel injection setup, although some people are more comfortable working with carbs because they're easier to understand. On a Miata, there's no good reason to pull the fuel injection or the distributorless ignition. On a Locost, there's a bit more reason although it will (ironically) cost you more money.
For mounting the carbs, use the same adapters that people are using for homebrew individual throttle body setups. I have one from Boig Motorsports, but they're more expensive than some others. TWM can probably help out as well. Regardless of source, they'll typically have a Weber flange on the end.
For a distributor, that's easy. Mazda (and Ford, and Kia) used a dizzy on longitudinal applications. It plugs right in to the Miata head where the cam angle sensor is now. Then you'll have managed to downgrade your modern fuel and ignition system to the same level of sophistication as my 1960's Land Rover