Subaru went to the library to look at Gluttony's book so he could find out how to fix Rem directly from the source but somehow Gluttony found out and ate his memories?

LOTTA holes in that, but so far it's only been Gluttony's powers that have been able to affect people's memories (unless you count Return by Death resetting everything)...well actually, the sanctuary tests messed around with memories a little too...hm.

It does make a little sense though, they're there largely to restore those affected by Gluttony's power to normal, Rem's coma and Julius' removal from everyone's memories. Subaru realizes something and goes to the library, where he loses all his memories since coming to this world. It stands to reason that he went there to read someone's book. Rem isn't dead, Julius isn't dead, the sin archbishop of gluttony isn't dead, but the Witch of Gluttony herself IS dead, and if anyone is powerful enough to interact with Subaru through the book of memories of their own lives after their deaths, it'll be a witch. My other guess is he looked at Regulus and/or Beetelgeuse's book, as they're also directly connected to and likely interacted regularly with the sin archbishop of gluttony.

I think that moment of realization before Subaru woke up without memories is important. His behavior in Meili's memories resemble other archbishops, so the "other Subaru" who's been acting independently is likely just an archbishop possessing his body, so it points to whatever happening before them being related to the sins or their archbishops in some way.

Not one, not two and not even three but FOUR Archbishops of Sin in one story arc?

I have no idea why he became the first character from Re:Zero whom I drew...