If you actually had the technology to accelerate to a speed close to light, time dilation might actually allow you to make an intergalactic journey as long as you were okay with leaving behind your home forever... Since a few years for you might be tens of millions of years elsewhere. There is also little matter between galaxies, so the hyper velocity particles problem would be less severe. Still total sci fi from where we are sitting, just saying that once you approach c distances shrink a lot (relative to your frame of reference). So if travel close to c is possible at all, travel almost anywhere is possible.

This is one of the reasons the Fermi paradox is so interesting. There are tons of possible explanations. One simple one in this context is, of course, that accelerating to speeds that close to light is just physically impossible for various reasons. This would at least limit migration to nearby interstellar distances at best, which when combined with other factors would make intelligences encountering one another statistically rare in the universe.

There was a sci fi book where a ship's Bussard Ramjet got stuck in the "on" position and they kept accelerating until time dilation allowed them to survive a great crunch and another Big Bang. By the time they stopped they were in a new universe.

For starters, let's begin with the first point it makes; If there are a bunch of civilizations out there, why haven't we heard them yet?

That's the wrong question. It makes an incorrect presumption; Why should we have heard them? Do you think a highly advanced civilization is going to be using something as archaic as "radio signals" to communicate across vast interstellar distances? Due to the inverse square law, it's incredibly inefficient, laughably so. It would be like trying to use smoke signals to communicate across oceans. A beam of light would be more efficient. But the beam would be instant and you could never "listen in" unless you were physically at the location of the target.

And who knows what else, maybe they communicate with gravitational waves, or something else we haven't discovered yet. Perhaps something with quantum entanglement (although that's unlikely). Yet, all of those cannot be detected unless you were specifically the target of the communication. They're not like radio waves where you can listen in. That's actually the very reason why they're so inefficient, they're broadcast omnidirectional and that takes a lot of power - wasted power.

And that's only one of the incorrect presumption Fermi's Paradox makes. There are more. I don't know why people keep bringing up the term when it's no longer applicable given what we know now. There is no paradox. There are plenty of great reasons why we haven't detected aliens yet, and none of them are paradoxical.

It does no such thing. Your objections are in fact a possible answer to the "why" posed by the Fermi Paradox, but they are pure guesswork.

The entire point of the paradox is to illustrate that the common (at the time it was formulated) ideas about the likelihood of life elsewhere were clearly wrong in some way or other, but we don't know what we got wrong.

We still don't know what's wrong with them.

A "beam of light" is governed by the inverse-square law every bit as much as radio signals are, both being propagating electromagnetic waves. It might be "laughably inefficient" (compared to what, though?), but it seems to be what we're stuck with. "Perhaps advanced civilisations use magic to communicate", is what you're basically suggesting. Well, maybe they do. Ultimately, we can only search for ETIs with the physics we actually know.

So, you're right to say that Fermi's "paradox" (always a bit of a misnomer) doesn't prove the nonexistence of ETIs, but you can't wave away fundamental physics because it gives an uncomfortable answer, either.

I also wanted to note in passing that it's a bit funny to obsess about efficiency and then throw out a statement like "maybe they communicate with gravitational waves". The state of the art gravitational wave detectors are targeted at finding signals generated by the merging of pairs of supermassive black holes at cosmological distances, and possibly neutron star or black hole mergers at galactic ones. If a civilisation is capable of smashing black holes together to send signals out a few megaparsecs, I would submit that efficiency is the very last of their considerations. Gravity is much, much weaker than electromagnetism.

Indeed, there are a lot of reasons to think that radiofrequency communication would be preferred. The galaxy is largely transparent to radiation at the hydrogen hyperfine transition at 21cm, a very useful way to cut through the crap and dust of the interstellar medium. By contrast, at optical frequencies the extinction from our environs to the galactic centre is about thirty-five magnitudes, roughly a loss of 10^14 in signal power. Radio receivers are relatively inexpensive and cheap to make and operate. The Arecibo dish itself could communicate with a similar setup thousands of parsecs away. Probably more now, after the receiver upgrades from a few years back.

But you're right that we shouldn't focus on radio communication with ETIs to the exclusion of everything else. Some folks have been discussing "optical SETI", looking for laser/maser signals whilst piggybacking on other observations. The SETI folks aren't stupid. But they're not well-funded, either, and they do what they can.

They're not like radio waves where you can listen in. That's actually the very reason why they're so inefficient, they're broadcast omnidirectional and that takes a lot of power - wasted power.

Radio dishes are not in any sense omnidirectional. They have a beam pattern which dictates the sensitivity of the instrument as a function of distance off-axis. You're right that broadcasting an omnidirectional signal would be a tremendous waste of power, which is why no one does that when sending signals over great distances.