The Casimir effect is about creating a spacetime "corset" so to speak, that is so tight that even the regular quantum fluctuations don't have "enough room to pass", so they "almost freeze", and when they "come out on the other end", they could for example break or delay entanglement?
On the other hand I think your assumption about the time aspect might be correct as we are talking about spacetime after all. The biggest issue might be that measuring time deltas might be harder than space deltas?
Regarding working with time-interval, it might as well just be the opposite: minimize space-interval and maximize time-interval for maximum effect. It's just wild guesses at my side. But minimizing time-interval should be trivially doable by just slinging the plates past each other at high speed.
Relatively more or less dense "things" (to each other) will always generate positive curvature of spacetime. What you want is relatively less dense area than vacuum in another region of space, since vacuum is (for now) what we constitute as (somewhat) flat.
That's what Casimir effect tries to accomplish: define a small enough region of spacetime where some larger quantum fluctuations don't have enough space to happen, thus lowering its energy below vacuum.
Since the idea is to define small enough space-like interval in spacetime to curb some energies off, could defining small enough time-like interval help the same purpose, multiplying the former?