Because of this dragging effect, an object within the ergosphere cannot appear stationary with respect to an outside observer at a great distance unless that object were to move at faster than the speed of light (an impossibility) with respect to the local spacetime. (Source)
The Good, the Bad, and the Ugly
When Sergio Leone directed that Clint Eastwood movie, little did he know that he'd created one of the most useful phrases in human history.
You're asking us if an idea is scientific but, per the quote above, your idea is based on a scientific impossibility. So, no. Your idea is not scientific. I can't even imagine how to get black holes to line up in a straight line in a universe where everything is in constant motion and, generally, a circular motion.
Everything you're talking about is a best-guess based on mathematics and remote observations. One of our celestial machinists could give you a boatload of math I can barely remember from college to explain the what-you-can and what-you-can't of the situation. But the simple truth is that there's no empirical evidence the consequences of the ergosphere are correct.
But this being bad is actually good for you! The fact that there isn't any actual science (per se) behind the idea you're trying to exploit means you can exploit away.
The number of people who will read your story and know to judge that it's not scientific is darn close to zero. Of those (assuming you have a well-written story) the number of those who will judge you for not being scientifically perfect is zero.
And I'm a fan of reminding people that what we know of science is far from gospel truth. We're constantly learning new things and discovering hidden mysteries. It's a huge mistake to believe that what we know of "science" today in any represents a cut-in-stone understanding — especially when you're dealing with massively theoretical things like what happens inside the event horizon of a black hole.
Bear in mind you're in great company. When Larry Niven first wrote about the Ringworld he didn't realize he'd written an entire story about a scientific impossibility. MIT students at a scifi conference marched the halls chanting "The Ringworld is unstable!" as if they'd cured cancer. What did he do?
He fixed it in his next book.
My point? This is a cool idea. Run with it and ignore anyone who thinks otherwise.