Hi Jake, welcome to the Sony Forums 
I'm not sure (I've not used a Rode before) but I'd say this was a audio gain issue, rather than a bitrate problem. As such there's no setting on the mic for it, it's something the camera deals with.
Unfortunately the NEX-7 (like all Sony alphas) only provides auto gain, so you basically have to deal with it in post-production. There are various tools you can use if you're interested.
I do know manual gain is something many alpha users have requested and there's always a chance it will be included in a firmware update.
As I say this is just a hunch, but it sounds like the most likely explanation.
Cheers
Mick