By adding a trimpot at the input of the circuit (1 - 100 ohm, 10 turn was the smallest I could find), I was able to tune the resonant impedance to very nearly 50 ohms. The resistance I measure across the trimpot at this setting is 4.6 ohms, so the resonant circuit is still getting >90% of the power. I was wondering if adding resistance at the input would decrease the Q of the circuit and thus lower the resonant impedance instead of raising it, but I guess it makes sense that it doesn't because it is not in the path of the resonant current (which just circulates between the inductor and the EOM). It is also interesting that the resistance I added is more than the difference I had before (i.e. 4.6 > 50 - 45.9). I guess this could be due to some parallel capacitance in the trimpot or due to a change in the Q of the resonant circuit from things like fine-tuning the resonant frequency.
About the RTV, I am hesitant to do it at this stage because we may want the freedom of trimming the impedance or resonant frequency in the future. It will be hard to access the tunable components if they are buried in goo. I think this can probably wait until we are sure of the final configuration. Also, since we are now PCB experts it may be worth designing a simple resonant circuit board that can be used for this type of application. Then, we could solder things in so that there isn't much rattle.
Here is a plot. I am not sure what the junk is at just below the resonance, but it is real (or at least reproducible). My guess is that the oscillator linewidth is sufficiently small for this not to matter.
After looking at the impedances seen in all the different configurations, I decided that the most recent result just didn't make any sense. So I re-took the measurement, and the impedance magically came out to 46 ohms (see below).
What I think happened was that I changed the frequency range of the sweep after I had completed the calibration of the impedance test kit, so the analyzer was extrapolating out to where I was measuring. Another thing I noticed was that the results were different depending on whether I used single shot or continuous triggering. This final result was done with proper calibration and using single shot the way I was shown to do it the first time.
Finally this business can be put to rest (unless there is reason to believe that 46 ohms is not close enough to 50 ohms---I'm not sure what sort of reflected power we are likely to be able to handle.)
RA: 46 Ohms is OK, but not too hot. How about trying out some trimmable components too? When you finish, I recommend filling the box with some kind of goo (like RTV) so that it doesn't all rattle around. That's what the professionals seem to do.