The lengthy discussion about getting the lenses of Sony RX-100's close together inspired me to draw up a crude diagram of my idea for mounting such cameras base-to base. As George noted, the tripod mounting hole is not aligned with the lens, so a single short threaded rod will not align the cameras. My idea is to mount the cameras base-to-base on a single aluminum bar, using flathead machine screws, their heads countersunk into the bar. You would position the cameras at a right angle to the bar, insert the screws, and screw them in until almost tight. Then you would rotate the cameras clockwise into their proper position on the bar, and engage a small clip or retainer at each end of the bar to prevent further camera rotation.
The anti-rotation clips at the ends of the bar would have to be sized/shaped to cradle the end of the camera farthest from the tripod socket. They could be attached by a screw or just slide onto the bar. (An even slicker arrangement would be some kind of spring clip.)
Unfortunately, I don't have any cameras with offset tripod sockets to try this out on. (Although I recently acquired some Canon S-95s, whose sockets seem to be offset about 3mm from the lens centerline, too close for this scheme to work.)
Looking at a dimensional illustration of the original RX-100, it seems this arrangement would give a stereo base of about 65 mm, if you used a 1/4" thick mounting bar. Of course, you need to be willing to take photos in portrait orientation. If you crop down to a 4:5 horizontal rectangle, you still have over 10 megapixels to work with.