Well, it's an inescapable feature of every chase scene (other than car chases or the like where there is an environment that affects speed) that the party doing the chasing decides the speed. If the fleeing party is faster, she flees, and there's no chase; if the fleeing party is slower, she is caught, but there can be a chase if the chasing party so decides. If both parties are equally fast, it's a dream sequence, because that's physically impossible; even slight differences in speed would rapidly put an end to an interstellar chase.
Indeed, if the chasing party feels he isn't
in control of the chase, he will smell a rat, such as in "The Survivors"!
Thus, in Trek chases, the chasing party would be motivated to ride bumper-to-bumper since the very reason he's chasing in the first place is to psychologically harass the fleeing party. If he were actually trying to shoot that party to pieces, he'd have done so already. Overshooting is an obvious risk, but one worth taking, because since you chase, you known you are faster and can afford an escape attempt or three.
"A tunnel of bent space stretching in front of the ship" sounds cool but isn't consistent with how it's done in Trek. Warp fields don't extend - they just surround. And indeed if one wouldn't need to stretch space all the way from A to B into a wormhole, and an extension of X ly would do the trick, why shouldn't an extension of two millimeters be fine as well?