Much will depend on the frequency range of the hum and on the frequency range of the Audio that you wish to preserve. This ARTICLE will give you some tips.
While I use Audition, SoundBooth (do you have that program, as it's included in most Adobe suites?) should be able to help, as can the great, little free Audacity.
You used a RED for home video?!?! (I'm soooo jealous.)
I've never used the MOV proxies from a RED, so I can't say their qualities will be any different, but have you tried the native R3D files at all? Do they exhibit the same hum?
Stuart - Just about any version of Sony's Sound Forge Pro has an excellent filter that can be used to remove or greatly reduce unwanted hum from audio tracks. It has up to four cascaded notch filters that can be adjusted for frequency and bandwidth. I have one filter set to remove 60, 120, and 180 Hz hum from sound tracks. - Bill
The audio files are *.mov for some reason, so Audacity didn't help either.
Open it up in Premiere and export the audio tracks as waveforms, bring them into Audacity (actually, you might try AIFFs... I've had trouble with Premiere wav output crashing Audacity) and do your noise removal there. It's tools are far superior to those built into Premiere, and I've had very little success with SoundBooth, either.