...given the saucer some kind of limited warp capability...
They really gave the saucer that from the get-go.
And not even particularly "limited" at that. The saucer reached Deneb IV only a few hours later than the stardrive section, despite back-backtracking a significant interstellar distance. Remember how, when faced with Q, Picard turned around and ran from him at higher-than-recommended-maximum warp for several minutes? The saucer would have had to undo that. Ergo, significant warp capacity.
The idea of the saucer as being capable of whisking most of the crew to safety at warp is reinforced in "Arsenal of Freedom". We further learn that even when released at impulse, the saucer can attain interstellar speeds all on its own, and successfully reach a distant starbase. (If this were not
the case, LaForge should be shot at dawn for not giving the saucer an initial warp boost before separation.)
This all jibes well with "Heart of Glory", where Riker sees a risky situation and recommends preemptive separation, yet Picard argues that there is time to utilize the saucer's escape abilities later, when the threat has been either confirmed or dismissed.
Other episodes or movies flow with this... Only "Brothers" discusses the details of dropping the saucer from warp to sublight, but this is in the specific context of forcing
the saucer out of warp. I guess we could argue, based on "Brothers", that the reason the saucer is docked to the stardrive section rather than merely flying in formation with it is that the mighty warp engines of the saucer are normally idled for economy and take time and effort to rev up.