I stopped by my dealer today and they took a quick listen. They're thinking it's an exhaust leak from the header gasket on the left cylinder. So, I bought two exhaust gaskets and will replace at least the left one this weekend.
I'm sure I could have asked about getting it covered under warranty, but the gaskets weren't that expensive and this way I'll have it done quicker and with less hassle than trying to schedule a time to drop it off at the dealer.
An exhaust leak is something that did cross my mind since the sound does appear to be coming from where the header meets the cylinder and the fact that it's only on one side. I tried tightening the exhaust bolts some weeks back, but both were snug so I kind of wrote it off. I'm hoping that this is problem and the gaskets are the solution. I'm wondering if maybe this happened after my wife dropped the bike on the left side? It would be a reasonable explaination, although I didn't start hearing the noise until a few weeks after the drop.
For this diagnosis I decide to go to the other Denver area Triumph dealer, Erico Motorsports. Very nice dealership with a nice vintage feel to it. Not the most convienient location, at least not for me, but worth the extra effort. People were nice and for a moment I didn't think they were going to let me go back to work, just keep talking my ear off!