If we're an amnesiac exile, self-sufficiency and avoiding tanking things with our face will be key to success.
I think those keys to success would be better taken care of by, respectively, the Utility Caster option for ourselves and the Defender option for our Eidolon. Not to say your vote isn't a fun and effective combination, just that it addresses different concerns, in my opinion.
I'm not particularly experienced with Pathfinder, so feel free to correct me on anything, of course.
The Summoner's most important ability score seems to be Charisma, so for synergy reasons (and of course also because being good at handling other creatures non-violently opens up a lot of venues), my first pick for ourselves would be the Face.
For the second one, I'd say we'd need something more combat-oriented, which kinda excludes Utility Caster, and to a lesser extent, Librarian. Melee Striker sounds dangerous and not very fitting, so I'd leave that out as well. Between Ranged Striker and Support, both for personal preference and for class-synergy reasons, I'd go with the latter nine times out of ten.
As for our Eidolon, being a Ratfolk makes us decent at scouting by default, I believe, and I envision the rat swarm as somewhat nightmarish, which would be a bit of a waste on something that wants to go unseen, so I'd rather not pick Scout. As a Support, I'm not entirely sure what kind of buffs/debuffs we would start with and reasonably get early on, so I can't say whether it would be easier for us to make our Eidolon tougher or stronger, but based on that, I'd consider picking the opposite option (so Defender if we could make it stronger and Melee Striker if we could make it tougher) to shore up its weakness.
So, for now, my vote would be:
[X] Plan 'Greater than the Sum of Our (Many) Parts'
-[X] The Face. It's not like your Eidolon is going to be doing much talking, despite having your languages.
-[X] The Support. Whether you're buffing or debuffing, you exist solely to maximize your Eidolon's potential.
-[X] The Melee Striker. Demolish your foes.
@Siberys , is plan-voting allowed?