I still say that since they're going with no canon ending....
The Illusive Man has had full access to the reaper tech needed to get us there. His team on the Derelict Reaper in ME2 could have taken scans of the reaper's mass effect core and FTL drive. Thus we would have the means of doing this lengthy travel without discharging. If we have the plans, we can build it. An ark to preserve the remnants of galactic civilization is something TIM would get behind, and he was banging an Asari Matriarch weekly.
I know it's a bit of a stretch, but since Bioware is weaseling this plot to get out of dealing with the endings anyway....
Asari Matriarch (smoking cigarette): That was great, Jack. Say, you haven't happened to come across anything new lately in your study of the reapers, have you?
TIM (taking a drink of bourbon): As a matter of fact, dear, I have. Let me show you. (grabs remote shows reaper drive and mass effect core drawings on the screen)
Asari Matriarch: What if I told you that the Council really did take the warnings about the reapers seriously and are working on a contingency plan to save galactic civilization? A drive like that would make it possible.
TIM: Really? What exactly are they doing?
Asari Matriarch: They determined that there is no way to defeat the reapers conventionally, so they're building an ark and will select the 100,000 of the best and brightest from each race and go to Andromeda if the reapers invade. We even have the cluster selected.
TIM: An excellent contingency plan, but I have other ideas. I think we can stop the reapers. But I'll give you the plans, and I'll also send a team of scientists, engineers, and workers to help with the project: The same team that built the SR-2 on one condition - that they're among those going to Andromeda.
Asari Matriarch (running her fingers up and down his chest): Thank you.
TIM: (Smiles that evil smile and lights a cigarette)
This solution solves two of Mac Walters' problems: Getting us to Andromeda, and getting Cerberus to Andromeda. Cerberus is an idea. You can't kill an idea. Besides, we need human mooks to kill and not feel bad about it.