Another problem is one of timing. If an arc is sent through the relays to Andromeda before the Reapers blockade Earth, that makes no sense--anywhere you go through a relay is still "Reaper Space" and offers no hope of escape. If it is sent after the Reaper War ends, then... why?
It couldn't be sent through the relays, unless what they discover is that some ancient civilization even more advanced than the Protheans (hey, the Reapers are lazy) actually managed to create a relay AND somehow get to another galaxy (via hand wavey space magic) to put the second one of the pair there, and used it to enact a mass exodus in secret during the reaper invasion.
Because, as you point out, having it be Reaper made doesn't make sense, and there is no way that anyone would think going through it to a new galaxy would be enough to escape the Reapers...since they created it.
Honestly, if they go the relay route they will probably just say "yo so we discovered a new relay and it took us to Andromeda. Whaaaat? Sh*t be crazy bro." and not explain it further than that, leaving us to fill in the holes with speculation.
That's why I think taking the long journey through space makes more narrative sense. They arrive hundreds of years later, they have no idea what happened in the milky way (thus ME3 endings are avoided entirely) and fast forward as they colonize a new galaxy.
The problem is they would have to abandon the relay network or discover that some advanced alien race in that galaxy created an analogous network. That would actually work enough to satisfy me.