Your partition keys can be composite, have a look here:
I agree with your other pain points - in terms of not being able to get counts, secondary indices etc. However, you can easily simulate some of those - maintain your own summary tables, indices and so on. These ought to emerge as platform features pretty soon though. It's not perfect, but its feature set is close to Dynamo.
As for Mongo DB, I guess this service has been built from ground-up to provide the availability guarantees and automatic partition management features. I don't know if Mongo provides those. You could run Mongo yourself on Azure if you wanted to; there's even a supported solution done recently.