As others have said, you are assuming that they are using a 90 degree view, personally I thought it looked wider, but that could be a trick of the video.
Also again you are assuming that they can only travel at light speed or slower, when we can travel well beyond the speed of light at that point in time. So even if we JUST double their speed we halve the expected travel time to 5.5 years, now they have already been in route for about 2.25 years, so let's say they will be here within 3 years.
Now... Let's also look at another thing, we have no way of knowing that they don't have the ability to jump from the farthest relay in the galaxy to the Citadel. Seeing as they created the relay network, and the mission through the Omega 4 relay in ME 2 already show that they have advanced technology in the relays that we have not yet discovered.
I would say that it is a pretty good chance they very well could be flying into the Milky Way and that they could very well be sitting on the council's front door step in roughly 3 years and we would be none the wiser, if it weren't for one Commander Shepard and his 'reaper' theory. (sorry couldn't resist the finger quotes there

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So yes, if they were traveling at just the speed of light it would take them a heck of a long time to reach the Milky Way. However, due to the establishment of FTL travel, and that Bioware has established that in current species in the galaxy have drives that travel at 4000+ the speed of light. I would say that it is very safe to say that the Reapers are cabable of at least that if not significantly faster speeds.
Just my 2 creds worth.