Simplest: set up a single balanced mixer. With an oscilloscope, set trigger from the source oscillator, and view the waveform at the output port of the mixer (which should be null, if the mixer is balanced).
This tests everything at once, actually. It also has the downside of being comparative, rather than quantitative (measuring a single parameter directly). Thus, you can sort and rank all the diodes, using any O(N lg N) algorithm, or brute-force all O(N^2) comparisons.
You'd repeat the test at a different frequency, and a different excitation level, to control for differing Vf and capacitance.
Actually, the two effects should be visibly separate (a nice part about viewing the waveform directly!), and can't null one another (because Vf is a resistive, in-phase effect, while capacitance is a reactive, out-of-phase effect).
Just under one test condition (excitation and frequency), the well-matched diodes should be pretty obvious, from the cleanly nulled waveform. Those with similar Vf, but differing capacitance (or vice versa), will have one part of the waveform (like the flat part in forward-bias) well matched, but the other part lumpy, and so on.
And, a null needn't be comparative; as long as you're inspecting that waveform there, you can read off the difference in Vf directly, or the difference in capacitance that's bleeding through.
Do make sure the signal source is, itself, well balanced, though! Do it at a modest frequency like 1MHz, sine wave (low distortion), and use a CT transformer to generate the opposite phases. Follow this up with a common mode choke (if nothing else, wind some twisted pair through a large ferrite bead, tens of turns). Then terminate the now-well-balanced signal currents into equal (precision) resistors to ground. Then, and only then, introduce the diodes (and a load resistance on the output port side) to measure them.
This sounds kinda fun. I almost want to set it up and do it myself!
Tim