Rather than adding more cameras, just add some mirrors.
The problem you have is that you are trying to do tomography with an under sampled system. This is a VERY broad subject - a bit outside of the scope of your question. But mirrors will work. I would recommend that you place them so the images are all in focus - depending on the depth of focus of your camera you may need to play with the "direct" path as well. But for example four mirrors set up as a pair of periscopes would allow one camera to take two images from +- 22.5 degrees. A second setup at 45 degree from that would give two more views for a total it four. This will reduce the degeneracy.
Here is a diagram of what I had in mind:
You can actually buy a device similar to this - see for example https://www.lhup.edu/~dsimanek/3d/stereo/3dgallery5.htm which includes some examples of the pictures taken with the Loreo stereo adapter - it includes a picture not unlike the beamsplitter I drew. Note though that they have the two sets of mirrors offset slightly, and that they are aimed "straight in front". This ensures that the focal planes for the two sides will coincide, but it also means that you may have a hard time getting very close to the subject - although the stagger may help with that. At any rate - I suggest you play around with the setup (using a small bead the size of your drop) until it looks right with a normal camera, before trying to do this with the high speed camera.
It occurred to me that since the drops are quite small, you might be able to simplify the setup with a pair of prisms - the basic idea being that a prism shifts the angle of the light between input and output. It might be tough to get the image you need (magnification, distance, ...) especially since a simple prism bending light through a large angle may have significant chromatic aberration which will make measuring the dimensions hard. Unless, of course, you use a monochromatic light source (or a filter on your camera). If you have a digital color camera you could see whether looking at just one of the R,G,B components of the image would give you a clearer image...
If you include a flat part in your prism, you might be able to increase the number of views to 6, spaced just 15 degrees apart. And since the "straight through" view is then coming through the prism, I believe the optical path lengths will in fact be the same - because basically the prism is a "very crude lens" and lenses do their focusing thing by having the same path length for all rays from object plane to image plane.
These are just some late night thoughts. If you have a buddy in the optics department he can probably come up with far better optical arrangements that achieve the same thing. This is really a bit like making a stereo camera - it's been done as the above link shows; and there is a company that makes attachments for various cameras - they may be able to give you exactly what you need.
PS - although this is a LONG time ago, I took high speed pictures of water drops during my graduate studies - so this is a trip down memory lane for me (and yes I had only one camera and multiple mirrors... - but it was an Imacon that could do 10 Mfps and my 0.4 mm diameter water jets were going at Mach 6...)
Best Answer
The phenomenon you mention is called Noncoalescence, and there are many beautiful experimental examples of it (see for instance [1],[2]).
Indeed, droplets of various liquids may float on the respective surfaces for extended periods of time prior to coalescence. The problem of explaining why this happens has been addressed by Klyuzhin et al. a few years ago, with some attempts to explain it better than had been done in the past.
I quote, from this paper:
They then propose an explanation for this mechanism: