Suppose two parties $A$ and $B$, some distance apart and at rest relative to each other [...]
Wouldn't this communication channel operate instantaneously?
If the proposed communication channel were indeed found to mutually "operate instantaneously", as may well be found experimentally, then the two distinct parties $A$ and $B$ are thereby measured to have been co-located (coincident; not apart at all), instead of having been "some [non-zero] distance apart".
How does this not violate the laws of causality with respect to the speed of light?
The experimental determinations of the two parties $A$ and $B$ don't seem to "violate the laws of causality with respect to the speed of light" under any circumstance; regardless whether they find (mutually) "instantaneous communication", or not.
Also note that in (S)RT "the speed of light (in vacuum)" is primarily understood as the signal front speed of whichever communication channel happened to operate the quickest. This is readily identified as the familiar signal front speed of electro-magnetic signals if the parties involved, such as $A$ and $B$, are (thought of as being) constituted by electro-magnetic charges.