There doesn't seem to be a replacement
So uh, you kind of buried the lede here, BioWare.
Inside of their PAX East plans for Mass Effect: Andromeda, the developer has announced that the game's at-home/public multiplayer beta has been eliminated. They had signups and everything, and it's no more -- instead, the post simply states "we look forward to seeing you in Andromeda."
Uh, so that can't be good. While people regard betas as demos more and more, they're actually valuable tests for developers to ensure balance and gauge the stress of their server reliability. Granted Andromeda is confirmed to utilize P2P play rather than dedicated servers, but this doesn't bode well for the multiplayer element.
I just hope it's as optional as they're saying it is -- the contained meta-story for multiplayer should help.
BioWare at PAX East 2017 [BioWare]