Using FET probes, I was able to measure a transfer function that looks a little more like what I expected. There are only two peaks, but I think this can be explained by a short between the two capacitors (and two tunable capacitors) in the LC pairs, as shown (in red) in the circuit diagram attached. The measured transfer function (black), along with the simulated transfer functions with (red) and without (blue) the short are shown in the attached plot. The measured transfer function doesn't look exactly like the simulated transfer function with the short, but I think the difference can be explained by stray impedances.