A response from the Twitter thread on the possiblity of using wormholes to cross galaxies:
It's certainly an idea with possibilities. THough a few things I should point out:
First, I wouldn't use Haestrom as a base. The quarian/geth war heating up, and Haestrom being in geth territory would make it too dangerous. I would think Noveria would be better. Parassini mentions people are showing an interest in dark energy in ME2 and it would help justify Cerberus interest in the place in ME3. In addition, Noveria has a reputation of being a place where off the books experiements are run (see rachni)
Noveria also opens up the possibility that these things anomalies were being investigated before the Reaper invasion. Which would more neatly answer the question of "Why are we sinking resources into a purely theoretical project while we're fighting for our survival?" question. It's already been going on for years. But now there's a time crunch.
Some sound ideas here! Like I said, I personally don't care whether they justify how we got to the Andromeda galaxy or not, I just want Mass Effect. But it's fun to speculate, come up with some logical reasons, talk about Mass Effect stuff in general 
It still doesn't answer the question of how can we move so many people in secret, or why the Reapers never bothered with this,
Who knows really. It could be that they kidnapped people secretly on Noveria or across the galaxy. And like I said earlier, if the galaxy can somehow keep a project like the Crucible, which involves massive manpower, communications, supplies, etc. hidden and protected for so long, I think we can call it more than feasible for a private corporation operating under utmost secrecy on Noveria to do the same, keeping them hidden from the Reapers.
Iakus, one thing I've noticed is that you really enjoy having as much of an airtight seal around lore, continuity and logic as possible. I have to admit I'm often like this too. I study Sciences and everyone often complains that I over-analyze things and don't just think of the simple way out and appreciate the whole thing as it is. I let little details bug me. It's good that we think in this way for some aspects of life, but do you think this mentality might be inhibiting your enjoyment of games in general, or is it something more particular in Bioware/Mass Effect that has made you been pointing out many faults in the games?
When it comes to entertainment, here is what I think: games, movies, books, etc. all require a certain suspension of disbelief in order to work. Some stuff just has to go conveniently in favor of the main character in order for there to be an interesting story, or even a story at all.
Take the Crucible for example. Was it convenient that it suddenly showed up in ME3? Yes. Was it convenient that the Reapers, for all their supposed power, couldn't locate the Crucible and destroy it? Most likely.
That's in the same way stuff in ME1 and ME2 was convenient. Was it convenient that somehow, after all this time, and just when we needed it, we had a dead Reaper lying around that Cerberus had already investigated and happened to have the last piece we needed to go through the Omega 4 Relay? Yes.
Was it convenient that the Reapers, and Sovereign in particular, had absolutely no back up plan for the cycle besides using signals on the Citadel as a Mass Relay? After the Protheans scrambled the signal, Sovereign was delayed by thousands of years so he could build up the fleet and find the right organic (a supposedly inferior form) to finish a job that he could not. Or why did Sovereign simply not shoot a laser at him while he was scaling the Citadel tower? Saren knew he was Shepard was probably coming coming. Warning Sovereign to keep a few sensors scanning for Shepard couldn't have been that much of a hassle. The station was sealed, nothing to rush the Saren or Sovereign.
These may not be the best examples, but I hope you see my point. Suspension of disbelief is necessary for a stories to be told. For heroes to overcome the odds, for legends to be born. I agree that Bioware should try and limit these as much as possible, but expecting perfection in terms of plot hole coverage is unrealistic. No game, book or movie is immune to them.
Although, maybe this all too place before the Reapers ever invaded. An experiment gone awry. A secret project to find a way to cross systems without a relay via wormholes. Something goes wrong, a bunch of ships maybe even a planetary base vanish and are presumed dead. The whole project is covered up and abandoned. The survivors find themselves in another galaxy and never hear about the Reapers?
A very interesting idea. That would keep the Reapers from finding about it. Though it does raise the question as to why the previous cycles like the Protheans, who were so much more advanced than we were, never discovered it and left plans and research as a last resort method for future cycles to escape the Reapers. Luck? What made wormhole research suddenly possible in our cycle? Unless every experiment with wormholes goes bad? Then why didn't each cycle leave successive plans and research on wormholes in the hope that the next cycle can build on it, like the Crucible?
This kind of train of thought is exactly the type I enjoy discussing and debating, but it isn't the kind I expect Bioware to address. This is the kind I talked about in my last block of paragraphs above. Fun to talk about, but nigh impossible to make full proof and keep a fun game, IMO.