It's closer to 100,000 light years across (but what's another 20k). I don't need to watch the ending I've played through it and experienced it over 25 times. It is exactly what is happening. Once the Crucible energy beam starts ping ponging to 14 consecutive relays and cuts to the next scene, that's because the viewer can extrapolate that it's hitting all the active relays in the network. You really didn't expect that one scene to go on for a full 2-3 minutes so you could observe it hit every relay, did you?
And as far as the "shockwaves" go, that is the Crucible's energy being emitted into the surrounding systems. It's clearly demonstrated after the Crucible fires and the ball of energy is emitted within the Sol System, cut to the galaxy wide view to see it happening in every other system with a Mass Relay. How fast it's traveling is irrelevant. It's covering the area the shockwaves pass through.
And as far as your miniscule percentage of how much of the galaxy Citadel space covers.....keep in mind you're speaking of the current cycles "Citadel space". Whereas the space the Reapers have been harvesting for the past 37 million years(atleast), consists of the entire galaxy. The civilizations that came up with the Crucible were from all over. They did not just hail from the same systems as our current cycle. So, know that the Crucible's reach is not limited to the fraction of space the current cycle has explored.
Actually, the range is around 100k to 140k ly, depending on what arbitrary factors you choose in include. We're still talking the same order of magnitude, though, but if you want to nitpick, then fine, we'll go with 100k.
Yes, you can claim an expectation of extrapolation and inference, but that goes both ways. You can assume that the links go from 14 relays to millions, whereas I find it more sensible to think they go from 14 to a couple of hundred. I don't expect it to show every relay being hit, but if we are to infer that every single relay is hit, I expect to be told that; else, it's open for narrative development.
The speed of the waves is extremely relevant; if that's truly a "God's eye" view of the galaxy, you're seeing a sight that no one in the story, even the Reapers, have ever seen; that shot is taken from deep in intergalactic space. At that point, it's fair to ask what timeframe the shot exists in. Are the waves moving at the speed of light? If so, and we're seeing thousands of years going by, then most of the galaxy will remain unaffected for quite some time. If, as you believe, we're seeing this happen in real time, and a magical wave of energy rewrites the entire galaxy in a matter of moments, well, then anything is possible, because that kind of event is Godlike in power. If humans truly built a machine that instantly rebuilds a galaxy's worth of life, there are essentially no limits to ME4. It's far better to view that shot as a representation drawn by the Normandy's galaxy map, showing propagation but overemphasizing impact.
Finally, when I say "minuscule", perhaps more clarification is needed. First off, all the civilizations have been centered on the Citadel, limiting them in galactic geography to the same capital, every single time. We know there's lots of overlap in civilizations, because old artifacts (and dead Reapers) turn up in Citadel space. We also know that many star systems are visited but not explored, and that exploration is limited by available mass relays; as an example, in order for the current cycle to explore a million stars before being Reaped, the Citadel Council would have to visit 400 new stars every year for its entire 2500-year history. Also, there's no guarantee that all cycles are 50,000 years; early cycles might have been 500,000 years long, or millions of years long, however long it took that cycle to get around to finding the Citadel (and certainly they were longer before the Reapers constructed the Citadel and relays).
BUT, let's be really generous, and say that every cycle is only 50,000 years long and takes place in a new part of the galaxy. Let's say the Reapers have been around for roughly (judging by the estimated age of the Leviathan of Dis) a billion years (you said 37 million, so I'm giving you a free 963 million years of bonus Reaping time). Even then:
That's 20,000 cycles of Reaping, one every 50,000 years. Even assuming each cycle develops a civilization that explores a million completely unique stars, with no star ever being visited twice, that's still only 20 billion stars...leaving 90% of the galaxy still completely untouched by anyone we know of.
P.S. - Yes, I know there are conventional FTL options that allow reasonably fast travel, but even then, I think I've adequately illustrated how very little of the galaxy the fictional lore has truly explored. Leviathan probably has more stories to tell, though...