Einstein never said we can't exceed the speed of light. He simply indicated that reaching the speed of light would cause the mass of the vehicle to exceed functional capacity. Actually exceeding the speed of light may not be all that difficult once we figure out how to live through it.

Second, it was Newton with his Third Law, not Einstein who said that every action has an equal and opposite reaction.

Third, a black hole is a misnomer. It is not a hole. It isn't even black. The color black is the effect of the absorption of all light frequencies. A "black hole" is in fact a huge gravitational force that absorbs everything. not just light. And it's anything but a hole. In fact, it's an incredibly compact ticked off rock in space that eats everything in it's path and there are literally thousands of them. One of them is the center of our galaxy.

Forth, space has no elastic properties whatsoever. The indented plane of a gravitational field is a visual metaphor describing change. Space is not two dimensional like a warped plane under a ball. A more accurate image would be concentric spheres of decreasing gravitational force around a single point in space. But that's boring to look at.

"I question how much space is elastic like" is what I meant to say, but have to say it here

since I can not edit my comment,..:(

I question how much space is elastic we can tell .it is not "elastic like" in the since that if we traveled at a fast speed and dragged space behind us, we would without choice be forced to slow down and be pulled back ..so I believe we can agree on that point. so space being different than an elastic, but possibly having elastic like qualities are these qualities enough to create a slingshot effect? lets pretend they are ..hmm..



lets consider the mass we are at, at the point of our instant stop.. and compare it to the space we dragged from behind and on the sides, even if space where exactly like an elastic we may be too "heavy" to be slung back, so space may just sling back without us... not ripping a hole in "the elastic"  since we are "immersed" in space, just we are not dragged back at a fast rate with it.



also consider  if we instanty became regular mass, before it flung us back... the force of the drag would cause an effect on the front and sides of us (the way we were heading before the stop) to want to keep us in place.. it would be kind of like air trying to keep us from being shot out of a slingshot except the resistance would be coming from the other direction. , and much stronger than air resistance,because it would be the very same elastic "stuff" trying to hold us in place, so this would at minimum slow our travel back and at worst stop us from going..so it seems unlikely to me that it would work as intended ....but who knows 



hope you understood what I meant I can be unclear at times for sure lol..

I can't speak to the physics of this, but as a long time fan of science fiction, it sounds like you might consider trying your hand at writing it.  This is as plausible as some of the other ideas I've read in some stories.