My question is: can I do it without buying a new bike?
-her geometry isn't touring standard. Is this something I can get around, or will I break my back before I've made it out of Maine?
No, not if it fits you and you are used to it,
-no bar-end shifters. I'd never even heard of these until a week ago. Are they really necessary?
No, IMO they aren't even desirable, but it is personal preference.
-only 20 speeds. is this really going to mess me up in, say, the Rockies? Or can I muscle through it (like I always do)?
The number of speeds isn't the issue. You may need to go to lower gearing. Packing very light can minimize that need.
-no disc breaks. all the literature seems to be up with disc breaks, but I can get away with good cantis, right?
Yes. Pretty much any decent brakes will be fine.
-she's carbon fiber, and for reasons I can't quite figure out, this isn't preferred for touring. question mark?
Carbon will be fine, just be carecul how you mount racks.
-lacking in pannier mount points (this is what her butt looks like: http://cdn.media.cyclingnews.com/2011/11/15/1/twells_specialized_crux_seat_stays_600.jpg). I've never mounted panniers before, but the guys at my local bike shop threw up their hands in horror. Are they right? Are there some sort of specialty panniers for just this purpose? Or could I just trailer it up?
You could use a trailer, but packing ultralight makes more sense IMO. See the link in my sig for some info on packing light on a road bike. There is an article on ultralight touring and some journals on tours ranging from heavy to ultralight
-700cc tires. I've heard 26ers are preferred because they're easier to get parts for. This won't be a problem in America, will it?
Not a problem at all.
...I guess there's two questions. One, is it even POSSIBLE to tour on my lovely bike, and two, would it make more sense to just suck it up and buy a (Trek 520/Surly Long Haul/Salsa Vaya/cue seperate discussion)?
It depends on you preferences. With my approach I'd rather use your bike than a LHT.