It's important to note the knowledge Einstein had access to while he was alive. People like to refer to his ideas as the end all rules about space and light speed, but his perspective was formed when we were still pretty ignorant (at least by today's standards). I wonder if any of his ideas would be different were he alive today. The simple fact that greater than light speed momentum has ever existed at any point kind of puts a dent in his whole theory, in my opinion.
It's also possible that getting around the universe will be more about ripping a hole in space and teleporting there, making light speed kind of irrelevant. Scientists have already observed that quantum teleportation is possible, so how much of a leap is it really to find a way to bring that to a macro level that we can control? Technology proves the impossible to be possible on a regular basis. There is no telling when we will stumble upon some new discovery that unlocks a plethora of options we never even considered before.
Space, as opposed to matter, does not have "momentum" in the sense that matter does. Ergo, even if space is expanding at a rate greater than the speed of light, that says nothing about whether "greater than light speed momentum" has ever existed.
How much of a leap is it to bring "quantum teleportation" to the macro level? Much larger than the leap from Newton to Einstein. Also, "quantum teleportation" is not the same thing as Star Trek teleportation. In particular, it relies up classical movement to set it up and therefore cannot be accomplished faster than the speed of light. I'd suggest a little more reading on the subject first.
And I doubt that Einstein would change that many of his ideas were he alive today for the simple fact that to-date most of his theories have been tested and passed the test. And no, before you set up that strawman, I am not saying that Einstein is infallible, nor am I saying that he would not have further developed his ideas were he alive today - no doubt he would have pushed his theories further than he got them - but I am saying that the fundamentals of his ideas are sufficiently solid that any newer theory must incorporate them as, at the least, special cases, in much the same way that Einstein's theories incorporate Newton's theories on gravity as a special case.