Finally got back to this after a while and made all sorts of measurements, first DCR with my good meter in 4 wire mode, then L with the LCR meter at several frequencies, then I went through with my sig gen set to 1Vpp on a 50 ohm load and swept through the frequency until I could see it was sweeping down, and it looks like it's shaping up to be a little different than is was first guessed. Then I sacrificed one to count the turns and look for any other oddities.
The pictured side's red and green conductors I dubbed the primaries for my results, since they had the lowest DCR, but I'm not totally convinced they are, considering that they turned out to be the same number of turns. The same gauge wire is used in every coil and the E core is definitely a ferrite material.
For the "primaries" I measured a 0.1995 ohms and 104.9uH @100kHz on the red and 0.190 ohms and 95.97 uH on the green, both were 22 turns. Starting with the red on the left as pin 1 and working around it like a DIP, that means the "secondary" between pins 8 and 6 measured 0.2155 ohms and 154.90 uH and counted 28 turns. The other "secondary" on pins 5 and 7 measured 0.469 ohms and a whopping 963.2uH @100kHz and counted 70 turns. The two "primaries" with 22 turns are wrapped outermost, with the 28 turn "secondary" under an layer of tape and the 70 turn coil in the center.
Using that naming scheme, I swept through frequencies, from 100Hz to 4MHz, and found that, surprisingly, they seemed to be pretty high frequency devices. With the "fixed" output of the sig gen I measured the input on the primary tap being energized and the outputs of both secondaries with my scope using 10M impedance probes and recorded the voltage of all three points. The graphs are attached, but I found the peak output voltage to be at about 1.6MHz from both primary taps, but with the changing input voltage thanks to the sig gen supplying the device, I'm unsure if this point would actually be the peak of current transfer. If I take the same data and plot "efficiency" of the secondary voltage divided by the input voltage, the peak is much higher, between 3.25MHz and 3.75MHz. Assuming the sig gen is doing a good job seeing the 1Vpp on its output terminal, I also worked out the impedance of the "primary" (voltage on the device times 50 ohms) and its peak seems to be just around 1.5MHz. I don't know how valid or useful the efficiency and impedance calculations are, but conceptually I think they make sense.
Looking at the turns, could this actually be a transformer for a dual supply with the things I assumed are primaries as the secondary side and tying the middle two pins for a 0V point? That would make it a step down transformer, probably from the 70 turn side with a feedback tap as the 28 turn coil? Does that really make sense as a design? Could also explain the color coding on the output wires, perhaps.