Ever seen a trike like this?
 

Is there such a thing as a 2 person side-by-side SWB recumbent tadpole trike?

You mean like this one?

http://www.bikeforest.com/cb/cb.html

Hmm... looks like that one's a quad (scroll halfway down the page for the clear picture). I'm no designer, but it seems to me if you want a SBS tandem, a quad design will distribute the stress better than a trike of either configuration.