Andromeda Initiative briefings (6/6 Golden Worlds and Settlements)

The Andromeda Initiative is not "a few". It's tens of thousands of people. 
Rachni haven't reached the point of harvest yet, hence leaving them be during the Prothean cycle. 
Protheans were wiped out to the point the only survivors were a few dozen, not enough to repopulate and continue to advance. 
Leviathans are few in number and are in hiding, and once seen to be alive were hunted. Plus from what the Catalyst says it seems the Reapers may want some alive to observe their fulfillment of their objective, like a child looking to parents for approval after doing what they were told to do. After all they know the Leviathans won't develop synthetics again. 

This is assuming they even know in the first place... regardless look at the Rachni and Leviathans.  They were still able to develop and work their magic.  Granted neither seemed interested in AI but at the end of the day that has never stopped the Reapers before.

eighty thousand on the arks, out of a galaxy of billions, maybe even trillions.

They'd certainly know.  Even if this was a private project, something on this scale simply can't be kept silent.  The ODSY engine is a massive breakthrough in technology, it should have been all over the news.  

In fact, the latest briefing suggests that the Alliance, at least, is aware of the project since they'll be escorting the arks to the edge of the galaxy.

The Leviathans managed to hide themselves.  The rachni were captured and turned to serve the Reapers.

Does a satellite galaxy mean anything I said about them is incorrect? That they don't have a lot of stars? Don't have great potential for more resources or alien life? Aren't closer and less dangerous to approach than Andromeda?

No, it doesn't mean any of those things. Those are closer galaxies and it would have made more sense to travel to one of them before Andromeda. 

Fallible, sure, but the AI is way to big for them to miss.

Not just millions. The Rapers have been doing that voodoo that they do so well for at least a billion years. 

And yet things still slipped through despite the fact that reapers tried to cleanse everything. The reapers aren't perfect and omniscient. They also might not even care. I don't see why the reapers should've made stopping this a priority even if they knew about it.

Why would they let anyone escape their mouse trap? It's all designed to catch races reaching a certain technological point and then convert them into a new Reaper or destroy them. What's the logic behind letting a race (or races) they're trying to convert or destroy escape to another galaxy?

No, things did not slip through. That was the whole point about the Reapers and what made them scary. The whole point of the Mass Effect trilogy was that the sentient technologically advanced races were doomed unless they could somehow defeat the Reapers.

These guys just flying away willy-nilly takes away all the doom. It's silly. 

Races slipped through the Reaper mouse trap so often I half wonder if it was intentional.

I'll go with Option D: Bioware messed up and are trying to get out of that regardless or lore or logic integrity. 

Well at least there is another thread for that third one...