Absolutely not, mass can not exceed the speed of light, so if a rocket(made of mass) goes into the black holes event horizon it is too late, in fact at around 2r no object with mass can escape. Also, any acceleration would just make you go deeper into the black hole faster, not get you out.
This means you cannot use a rocket to escape from the event horizon once you have went past the horizon, as any acceleration would lead towards the black hole no matter the amount of acceleration(unless you exceed the speed of light before you hit the singularity, but this is not possible). In fact, to even just not fall in and stay still you would have to use infinite energy on the edge of the horizon, let alone actually inside the black hole.
So, in summary, you can not do as you say because you need to exceed the speed of light to even go away from the singularity once inside(not possible), you can not get further by slowly leaving as this slow, gradual escape makes you go towards the singularity faster, it does not bring you away.