The Problem with the Fermi Paradox is simply that it was never based on proper science.
Occham’s Razor says that if there is more than one possible explanation for something, the simplest one has to be assumed to be correct until it is disproven. The simplest explanation of all, that the universe cannot sustain life, has been disproven by our very own existence. The basic reasoning behind the Drake equation looks okay, so the “next-simplest” explanation would be that the probabilities used in the equation are wrong.
Which they are. They’re based on a highly biased observation of the distribution of stars and planets in our local part of the universe, which is not the same as in most other parts. There’s a blatant disregard for the economics involved with interstellar travel and radio communications, e.g. the amount of resources required to send a single radio signal or a spaceship just from one solar system to the next (a couple of nuclear reactors are not enough). Even if we assume the availability of nuclear fusion and faster-than-light travel, the universe is still an insanely huge place and any number of maybe existing civilizations is contradicted by the tiny, tiny probability of them reaching our solar system exactly within the last or next couple of thousands of years.
Drake never intended his equation to be a proper scientific thing, but wanted to “stimulate dialogue” so he could get funding for the SETI project. Which he needed because the SETI project doesn’t make any scientific sense and is considered a pseudoscience in the astronomy community. We have about zero reasons to assume that the universe is really booming with life, as even Peter Schenkel, a support of SETI, wrote in 2006:
“We should quietly admit that the early estimates—that there may be a million, a hundred thousand, or ten thousand advanced extraterrestrial civilizations in our galaxy—may no longer be tenable.”
The Fermi Paradox and the original Drake Equation are basically just being kept alive by pop-sci blogs.
(Gravity waves won’t help, BTW. They also just travel at the speed of light and you need much more energy and much larger equipment than for electromagnetic waves.)