Reapers in Andromeda

Reaping Leviathan was the AI's answer, as well as repeating the process every 50k years. Since the AI eventually concluded that Reaping was the only way to prevent conflict between synthetics and non-synthetic life then, yes, it's plan included reaping their creators. It says so in the EC. Nothing the AI says, or Leviathan says, ever mentions anything other than the Milky Way. There's a Leviathan quote where they talk about "their galaxy" and all of their thralls. Doesn't sound like any other galaxies were considered as a part of the problem by Leviathan. Since the AI was only interested in solving the Leviathans problem that would only include the Milky Way.

By the time the Initiative arrives in Andromeda either the Reapers are controlled, synthesized or destroyed. It's only in the EC that there's a refuse option, in which case they'll stay in the Milky Way and wait for their 50k year signal since that's their programming. That's the key, the Reapers operate according to programming from a central artificial intelligence. The only thing that would think of other galaxies is the Star Child and it never did in millions of years of existence. Since the Initiative isn't mentioned in ME3 then the assumption is that Star Child never knew about it either.

It was some really tight code? Maybe Star Child was never capable of thinking that far out of the box, past the Milky Way, even though the crazy machine seemed to be fully capable of independent thought? I wouldn't say it's a flaw in the story, just something that didn't need to be explored within the context of Shepard's story.

The thing is, the Leviathans may have been aware of intergalactic travel but didn't program the Catalyst with that possibility because a solution hadn't been found yet. Just in case they needed to change the programming to better design a solution. Of course, the Leviathans never thought that eliminating them would be part of the Catalyst's solution.

Just like how drugs get tested on a small population before being sold to the public. Just in case there are unknown problems.

Nah, I think it's more just lack of realizing that with the given data, that the Catalyst would use any solution they found on them.

The best way to prevent organic and synthetic conflict is to keep the organics from making synthetics and the only sure fire way to do that is to eliminate them before they are capable of doing so. If the Leviathans were able to create the Catalyst, then they are able to make synthetics. It was only logical that the Catalyst applied the solution to the Leviathans given the data the Catalyst had.

Well, they hadn't quite gotten the timing right on it. Javik did mention Synthetic vs Organic wars and of course there's the Geth vs Quarians.

And of course, even if they had, the Leviathans would obviously not be able to fall under that because the Catalyst is synthetic in the first place.

The main reason I think the Reapers don't go to other galaxies has nothing to do with any theoretical mandate to restrict their activities to the Milky Way. Instead, I think Vigil's reasoning makes the most sense. The Reapers retreat to dark space and go dormant. Once they start the harvest they're pretty much non-stop for however long it takes to succeed. Centuries, in the case of the the Prothean Cycle. I don't believe they have unlimited power. Hence, they sit tight at full power, waiting for the proper time.

The other side is that the MW itself could be considered the "testing grounds" for their solution to the organic vs. synthetic problem. Once they solve the problem they then move outward and apply it everywhere. It's only in the current cycle that they found the solution (Synthesis) so it's only if that solution is applied that the Reapers would then choose to go outward and force it on the rest of the universe.