I finally got around to re-modifying the EOM resonant circuit. Since adding a parallel resistance at the input didn't seem to work when I tried it before the holidays, I decided to try Solution 1 of Koji's suggestions from this elog post. Below is a picture of the circuit once I was done modifying it. It has 3 cascaded RF transformers at the input followed by an inductor (actually two in series) which is in parallel with the EOM to ground. The transformers are 1:16, 1:4, and 1:2, giving an impedance division of 16*4*2 = 128. Since (as explained in the linked post), the resonant impedance of the circuit without the transformers is estimated to be around 6 kohms, their addition should result in an input impedance on resonance of ~50 ohms. The plot below the picture shows that this is not the case; the result is closer to 140 ohms.

I assume that the problem here is the various stray losses from series resistances (e.g. in the transformers). I am going to take a look at all the data points we have from the various impedances measured using the various circuits and try and come up with a solution that will work.