And just in case anyone is curious, here is the issue I raised on the Parse support site:
Unlike here, the Parse employees jump right on open issues (I got an answer literally within 3 minutes). It appears that there is no workaround for the limitations in network.request that will allow upload of binary files to Parse (which I kind of expected, just wanted to verify).

[import]uid: 111481 topic_id: 31044 reply_id: 125199[/import]
Thought I’d throw it out there.