Well, I was right about the basic clutch adjustment being straightforward. But that doesn't mean I was able to figure it out on my own! Ha.
Even with the shop manual and the Haynes manual in front of me, I was pretty clueless on this one. Luckily the folks over at the TriumphRat forums were able to help me out. Check out this thread for a rather detailed explaination of the basic clutch adjustment. It's threatening to downpour right now but I'll take the bike out in a few days and see if the adjustment did the trick.
I'm starting to put together a document which captures the information I've come across on Triumphs so far, I'll host it and post a link here when it is further along.