I'm finally able to show some results after a few days spent trying to create the world's best balun. I had some pretty decent results, but ultimately I decided to reevaluate my strategy. I scrapped the original transformer jig, and instead dug another module out of the junk bin. This one has four sets of three cores when viewed from the bottom, and 12 pins per side. This leads me to believe that it's exactly what I was looking for, i.e. a center tapped transformer with CMCs on either side. It was in an unusually wide SOIC package, though, so I had to get creative and cut a SOIC DIP adapter board in half to be able to easily prototype with it. I hot glued the whole mess to a 0.7mm solid copper shim, and added a couple of SMA connectors. The result is shown below. (The solder looks like sheeit, but that's just where molten solder hit some runny hot glue. All of the joints are happy and healthy.)
As for the data, it looks to me about what I'd expect. S11 floats around just below 0 dB, and S21 is ridiculously low at the 1 MHz start of the sweep, gradually rising as the frequency increases. At the target frequency of 10 MHz, S21 is down around -42 dB. Between the rejection from a ferrite over the coax jacket and the "typical" 70 dB CMRR of the AD8130, it looks like this will be a great solution.
I'm thinking of making the whole signal path be symmetrical: Input coax --> CMC --> Transformer --> AD8130 (differential receiver) --> HIgh speed opamp buffer (OPA890?) --> AD8132 (differential cable driver) --> Transformer --> CMC --> Output coax. Due to the nature of a fully differential amplifier, the isolation between individual channels is compromised when driven from a common source (since the inverting output is fed back to the noninverting input, unlike a traditional opamp). The opamp buffer helps restore this.