OK, just correcting what I think is an initial misunderstanding…
Escape Velocity means that, with a single initial burst of energy, that energy must be sufficient to accelerate the object to 17,000 mph to clear Earth’s gravity well. Anything less, and the object falls back to Earth at some point.
Thus in a way, the initial concept is valid. The Saturn V’s did not need to hit 17,000 mph to clear the Earth’s gravity well. They just needed an amount of thrust (force) spread over time that, had it been released immediately, would have been able to accelerate the mass to 17,000 mph immediately.
Now, just outside the Event Horizon of a Black Hole, the escape velocity is a fraction under 186,000 mps (per SECOND).
Thus, to escape from JUST OUTSIDE the Event Horizon, you would need sufficent force applied over time to be equivalent to the force necessary that, if released immediately, would accelerate the object to a fraction under 186,000 mps.
Once you cross the Event Horizon, you need to be able to have enough thrust force to be equivalent to a one-time burst of the energy required to accelerat to greater than 186,000 mps.
The calculation for that force is infinite, since the amount of energy required to instantly translate an object to greater than 186,000 mps is infinite, based on Einstein.
An infinite amount of energy realease over time is an infinite amount of energy at ALL times.
Did that work for ya?