... Now to the technical, hopefully more interesting part!
Eagleworks has made a risky, but from my point of view, good, decision, to use a PLL-based driver and to reference the PLL directly from the cavity resonator by a sense antenna. Active frequency control has been proposed by many others here, but directly referencing the cavity resonance itself is, from what I've seen, a new approach. They don't make fuss about it, and in fact, it's only noticeable if you look at the block schematic of their driver more closely.
There is one thing that they really "nailed" with that design however: it's that the driver is self-locking to the cavity resonance and the resonance is basically self-tracking in real time to a very high precision. I'm not aware of anyone here attaining comparably stable locking by other means.
There is also one major and one minor disadvantage: Their system is free-running (major) and it provides no phase tracking (minor).
The major problem is that it will always automatically lock to the strongest mode in the vicinity of the initial "seed" (see paper for details on "seed") frequency. It's a basic, unavoidable modus operandi for their system. Given the way it is made, it cannot act otherwise. It's like a "greedy" optimization algorithm that will always continue searching along an upwards slope until it finds a local maximum (mode with highest field strength). If a stronger (e.g. TM) mode is nearby, the system can't stay stable driving a weaker (e.g. TE) mode, it will always self-lock to the strongest local maximum (mode). That's why, when they said that they "had difficulties" exciting a particular weak more, this would be perfectly understandable - their drive system is self-optimizing in real time along a rising gradient towards the strongest local mode and it has no way to turn this "feature" off. Basically they made a very efficiently self-locking driver and once that worked, in some respects they've fallen prey to that driver's good automatic optimization abilities.
The minor problem (rather unrelated) is that they implement a manual phase setting that is preset in advance and does not get the benefit of automatic tracking in real time. But this should be less difficult to fix (see below).
Some people here will probably make the point "So don't make the driver so autonomous!", but I'd rather for now explore the idea, how such an "autonomous" driver might be put to a better use - and I think there are ways for doing that.
IMO, the key to this is a cavity and antenna design that is strongly mode-selective. That is, rather than forcing a driver to excite a weak mode that is difficult to lock into, better make a resonant system that has a mode selectivity sufficient that the desired mode is indeed the strongest mode - then the "greedy" self-locking PLL driver will find it by necessity rather than by luck.
We've now had many cavity designs of "classical" shapes - cones with end plates. They all have strong "nearby" undesired modes in the vicinity of the ones that would be preferred. But there are other, more advanced possibilities, for example the parabolic, di-parabolic and hemispherical ones mentioned by Todd and Shell on page 129 (ff) of this thread, one example re-attached below for reference. I think that advanced resonator geometries should be worth consideration as they might provide a high mode selectivity among other things. Plus they may also provide high field strengths and some may be amenable to a high quality prototype production on a CNC lathe. I think that advanced resonator geometries should be in our future rather than in our past.
Also, there have only been single antenna systems used so far. Phased arrays can provide an orders of magnitude higher directivitiy than any single small antenna, and inside a closed resonator the antenna directivity will practically translate to a mode selectivity. By driving a resonator with a phased antenna array, it should be possible to greatly enhance the mode selectivity of the whole antenna-resonator system. Basically up to the point where the resonator accepts but a single mode, uniquely chosen by the geometry of the phased array. This should also be one of the things for future consideration.
And finally to that pesky minor problem of the missing phase control. As long as the frequency is self-locking, the phase angle can be adjusted rather slowly, the control loop does not need to have microsecond reaction times. It may be perfectly fine to measure the forward and the reflected power and slowly adjust the carrier phase to find the best match by an optimum operating point tracking algorithm. Since it does not need high speeds, a microcontroller could do that.
In fact, The Traveller (IIRC) has proposed to control the drive frequency to minimize the reflected power based on the reflected power meter readings. That's certainly a good idea, but it has its difficulties because it only controls frequency, not phase, and the frequency stepping must be very "delicate", especially for narrowband High-Q resonators, plus the control loop can be no faster than the reflected power meter.
However if the frequency is taken care of by a fast real-time PLL like in Eagleworks's design, the phase angle becomes a quantity like the power factor in mains electricity networks. It would be easier to control at modest speed and The Traveller's reflected power minimization strategy could just as well be applied to phase control instead of frequency. Eagleworks adjusted their phase manually and they reported seeing a "Phase Q", that they could maximize by tuning. That's a good start, but it does not track dynamic changes, and this tracking could be added by a relatively modest control loop running at manageable speeds.
As a summary, I'd like to include a proposed block schematic of a modified driver. It's strongly based on the Eagleworks design, but includes the phase control as detailed above (needs a continuous 360 degree phase modulator) and a little reminder that multi-antenna phased array drive might also be an idea to be considered instead of (or in addition to) an advanced geometry resonator to improve selectivity...
Obviously the entire thing with all bells and whistles would be spendy, particularly for a homemade build, but there are also some institutional EM-drive builders reading here, and who knows, someone may be interested at least in some parts and aspects as a way to improve his existing design. Plus, I think that it was time to sum these things up that individually affect the critical EM-Drive operating parameters, and mention them together in one place for easier reference.
Particularly regarding proposed superconducting resonators, where loading times are long, so must also be the phase coherence of the driver. Otherwise the RF source will start "unloading" the cavity as the phase angle drifts, before it even got fully loaded. To that end, one should consider both fast real-time frequency tracking and stable precise phase tracking in order to maintain a stable resonant field inside.
Regards