All we are really missing here is the exact mechanism by which the timehole disrupts the attempt at using the warp field for propulsion.
Contrary to popular belief, Trek has never supported the classic scifi idea that high gravity would prevent hyperdrive. We see ships warping right from the orbit of planets, sometimes from the atmosphere of planets, even; from the orbit of stars; and even from the inside of black holes, which indeed ought to be the no-frills, ho-hum way to escape those (VOY "Parallax").
However, warp close to high gravity in Trek is very slow. That is an obvious dramatic conceit: if we see a source of gravity such as a planet in the same view with a starship, the speed differential can't be too extreme! But in practice this means that high warp gives a sublight speed close to stars and the like (something we see especially clearly in those "time travel slingshot" adventures). Would the pull of the Red Matter timehole be enough to slow high warp down to a standstill? Even when a more ordinary black sucker in aforementioned "Parallax" posed no difficulty to a standard warp drive as such, there only being an issue with a weird topographic feature blocking their path?
Or does the exotic timehole indeed hurt the warp drive by a different mechanism, not just by slowing it down the "usual" way?
If the former, then shutting down warp would indeed mean losing the battle and getting pulled inside, as warp is the mechanism (feebly) fighting back the pull. If the latter, then warp may play no role at all, and it's just the impulse drive Kirk is (simultaneously) running that keeps the ship from being pulled in but cannot achieve more, not without the boost from the kabooms.
Of course, it may be that maintaining a warp field helps the impulse engines - we have every reason to suspect a key role is played by subspace field gadgetry that lowers the mass of the starship, and this gadgetry might just as well be the warp drive itself. Losing this advantage would briefly make the impulse engines struggle more - but OTOH it would return inertia to the starship, making the job of the timehole in accelerating the ship towards her doom harder, too.
Basically, technobabble from preceding Trek offers endless explanations for what happens here. And our heroes ought to be on top of most of that technobabble, even if the Scotty or Kirk of this movie never did a slingshot maneuver in their careers, or orbited a collapsing Psi 2000, or fought a black star. It boils down, then, to whether the scene appears intuitively acceptable or not.
Timo Saloniemi