Meteor is good. I don't have much experience with it, but it is good.
Meteor would do what my fork would do. But where I would use 2 frameworks (one for the client side, another for the server) Meteor is just one.
So yeah, it seems like a fine idea. It would bring pretty much the same benefits as my fork. Except it would be more consistent.
There is nothing wrong with MongoDB. NoSQL databases generally perform only slightly worse than properly normalized SQL database. MongoDB isn't the best for performance though, redis or Cassandra would be a faster choice. Both would probably work well with Meteor. Honestly, its not too difficult to swap in another NoSQL database if required, so I don't think that its an important design decision here, they all operate similarly.
NoSQL databases are nice because they don't require you to normalize them. You can nest data structures if necessary, and you can leave a document ID and join it later. They better represent the data than a series of tables that have to be manually assembled. I do think a NoSQL database better fits your graph structure than a SQL database.
Not familiar with Polymer. I'm not sure if its necessary. I guess Meteor might not provide enough DOM manipulation for Agora. Thats why I was using Durandal, to manipulate the DOM for to make it a single page app. I'm not familiar enough to say Polymer is good or bad.
TL;DR, Meteor should be fine. I can't speak for Polymer (Nor do I see why its necessary, but I'm guessing Meteor doesn't manipulate the DOM enough). MongoDB will be fine, especially initially. NoSQL databases are quite nice, I think the model fits your data better than a SQL database, and if you need more performance you should be able to swap a faster NoSQL database in without too much effort.
If the $650 isn't breaking the bank, go for it. It doesn't look like a bad decision. Just pay him in installments so you can see work is being done.
I'll still work on my fork, slowly (I have a lot of projects I like to work on).