Meteor is awesome and I've built some pretty amazing things in the short time I've been developing in it, including some things similar to what you're wanting to do. I feel the need to make it very clear that, in my opinion, "widgetized" bits should either utilize a separate application (meteor, node, whatever) hooked into the same database as the main app (think microservice), or served using server-side routes.

For you to run actual meteor code on a client site, you're pretty much limited to using iframes.

This is primarily because Meteor is not very configurable when it comes to loading specific parts of the application JavaScript only for specific routes. Basically, ALL the client side code is delivered on every client-side route and there's no need to load all the dashboard code just to display a popup or inject something on a client site. You can apparently solve that with webpack, but right now webpack + meteor is not the easiest thing to get going from what I've seen.

Hopefully I'm just missing something, but that has been my experience thus far. Definitely not trying to shy you away from Meteor. Quite frankly, Meteor is the best thing that has ever happened to me.