So, for an update... I thought I'd post my latest findings on this issue in the event someone else stumbles across this thread in the future.
Thanks to the fantastic service from Robert at Audio Eden I was able to procure a brand new Rega Exact under warranty -- hooray for that! Unfortunately however, it made no difference in the amount of hum I have in my system. The fact remains though that when I put an old Shure M91ed on the deck, the hum is practically gone. I thought maybe the output of the Shure was so much less than the Exact that it is just giving the illusion of less hum. Checking the specs shows the Shure is rated at 5mV and the Exact at 7mV. I don't feel this is a big enough difference to make the hum disappear.
I think it's safe to say that the cartridge was not faulty. However, I think it's also safe to say that the shielding in these Rega carts, regardless of how good it is, is not good enough to block out the amount of ambient EMI in my apartment.
My next step is to try and find someone around town with an Ortofon 2M or Dynavector cart who will let me wire it up temporarily to check for hum. If these cartridges block out the EMI in my apartment I'd be tempted to sell the Exact and get a completely different cartridge.
That said, any Montreal-ers feeling particularly generous?
Half-case of beer is yours if you want to drop by with one of the cartridges mentioned above, hehe.
I'll keep updating this thread as new info comes in. I don't imagine it will happen in a short amount of time though.