I've been using Meteor for a couple of years now, and although it does a lot of magic, I recommend using it only for very simple projects.

For this application, meteor may be suitable, but keep in mind that you'll need to build a lot of your supporting infrastructure until Meteor 1.0 comes out.

Reasons not to use Meteor:

It is currently very difficult to accurately profile memory issues.

Simple html mixups can take half an hour to debug due to the fact that they'll only show up in production, and in minimized/uglified form.

MongoDB costs 'money' to scale properly (sharding across multiple machines with lots of memory (if your database grows).

Edit: This is not a simple project, so maybe meteor is asking for trouble since it's not very mature yet.

Check the mailing list for this. There wasn't a large amount of discussion about mobile options when I last checked, but one solution seems to be what you've already listed above: Phonegap/Cordova.

https://groups.google.com/forum/#!forum/meteor-talk

It didn't seem like there's a "perfect" solution for this yet (in any realm--it's all still evolving).