As a trained physicist, I think you are getting this relatively right. Some of the issues at play are simply unknown according to the current state of theoretical physics.
Our Quantum Field Theories naively predict an infinite energy density all throughout space time. A naive guess at regularizing this leads to absurd predictions 120 orders of magnitude off [1]. So there has to be something else happening here. One of the things that supersymmetry brings to the table is that it makes this energy density exactly zero (but then it get's complicated because you need to break super symmetry...).
The thing is though, without gravity the absolute energy density of a quantum field is just some unobservable number. But how to reconcile gravity and quantum field theory is an unsolved problem to begin with, so it's completely unclear what that naive infinite number actually means. We are working without a firm theoretical (or empirical for that matter) foundation here.
However, the Casimir effect is remarkable exactly because it appears that the local energy density between two conducting plates is lower than in the ambient space. This is an energy difference that can and has been measured [2].
It is entirely plausible that it interacts with gravity in the right way to cause an effective negative energy density. This has been speculated by serious physicists for a long time. However: The Casimir effect is exceptionally weak. Space time is exceptionally hard to bend. So the idea of an actual warp bubble from Casimir effect geometry seems extremely far fetched[3] right now.
How stiff is space time? LIGO the gravitational wave observatory, measures changes to a 4000m distance that are smaller than an atomic nucleus, at its full design it will detect changes that are many time smaller than a proton. This is a feat of experiment that is the more astonishing the more you know. If you had told me you want to build something like this I would have assumed that it's likely impossible. Now, the first signal that could be detected by LIGO was a black hole merger that radiated away the energy equivalent of three solar masses. The peak power output of this event was larger than the combined energy output of all visible stars in the observable universe.
How small is the Casimir effect? Micro Newtons/m force gradients for micro meter distances [4]. Again we are talking about an effect so subtle that it's only been measured reliably in recent decades.
So these are the orders of magnitudes involved: White et.al. claim they can use an effect so small as to be barely perceptible, to manipulate space time in such a way to create interesting effects, when it takes the energy output of the entire universe to generate a ripple in space time strong enough to be detectable (a few galaxies over) by the most sensitive instrument ever devised. So I am sceptical.
[1] https://en.wikipedia.org/wiki/Cosmological_constant_problem#...
[2] https://en.wikipedia.org/wiki/Casimir_effect
[3] My physicist intuition says: Far fetched but not impossible. One of the heuristics for looking at this result though is this: The lead author is Harold White, one of the people who really pushed the EMDrive. The EMDrive is not far fetched but simply impossible (to a physicist the EMDrive is in exactly the same category as perpetuum mobiles). Worse, the original EMDrive paper by Harold White, despite supposedly showing evidence overthrowing three centuries of established physics, did not attempt to get published in a physics journal (which would have required extraordinary proof for such an extraordinary claim). Finally it involved some theoretical speculation that were just abject nonsense. These things mean I will not spend serious time on understanding and analyzing the details of this latest work.
[4] https://www.nature.com/articles/ncomms2842