I think it depends on what you did with the Collector base. If you saved it back in ME2 then yeah, there's no way that the Council, and by extension the Reapers, won't know that Cerberus are there. If, OTOH, you blew it up then it's not so obvious that Cerberus have been completing operations through the Omega 4 relay post ME2. From memory Shepard is surprised when they find part of the Human Reaper aboard Cronos Station.
In previous cycles the Reapers obtain their knowledge of who is where through the Citadel trap. Even though this didn't work in this cycle, the Reapers still achieve the same goal when they capture the Citadel at the end of the game. Of course that knowledge is imperfect, based entirely on what the Council/Citadel races/archives are aware of at the time of the Reapers taking control. Hence, if no one knew that Cerberus were going through the relay then it's questionable as to whether the Reapers would know. It's debatable whether the Reapers even knew where Cronos Station was. This was pretty much how the Ilos Protheans survived - records of their existence were destroyed when the Reapers took the Citadel in that cycle, and as such, Ilos was overlooked/forgotten/missed.
That being said, there ARE problems - first and foremost, as you say, the Vanguard. 12 scientists surviving on Ilos and covertly working to understand the Reapers' plan of attack is one thing - having enough people to go out and take control of the rest of the galaxy is another entirely. Plus, as soon as you start going about that goal, the Vanguard is likely going to discover the plan pretty quickly.
The other problem goes back to what you did with the Collector base - if you saved it, then it's a safe bet that people know Cerberus are there, studying it or otherwise. As such it's a matter of time before the Reapers figure out that they're there. If you destroyed it then there's a question over whether you have the technology needed to be able to survive at the galactic core. The Collectors got their tech from the Reapers, would any of the current cycle races have that level of tech?
TBH, there are problems, but it's still a plot that I'd have actually preferred than the one we got in-game.
Re the other point - I think they probably feel that they did as much as they could given the time constraints. I don't think it takes a genius to conclude that if you'd offered BW three months to get everything ironed out then they'd have snapped your hand off. Bottom line is, EA gave them one extension and by the looks of it weren't prepared to give them another one. At that point it was a case of finish the game as best they could. That's how From Ashes got separated out from the main game, and it wouldn't surprise me if they cut Omega early on as well for the same reason (before the first extension WAS granted).