Rode by the dealer earlier this week and the head wrench recommended that I unbolt the rear caliper and move it to the top of the brake disc (turning it upside down). He said that because the bleed nipple is at the bottom of the caliper you'll never get all the air out unless you do it this way (because air rises and settles at the top of the caliper... duh).
So, this morning I unbolted the caliper, loosened the rear wheel pinch bolts to give me more slack in the chain and more room to work, and then I saw that I'd have to remove the plastic guide under the swingarm that routes the rear brake line and the ABS sensor so that I could pull the rear caliper out and around to the exhaust side of the wheel where I could fit it between the spokes and slip it onto the top of the rear brake disc.
Once I did that I bled it normally from the exhaust side of the bike. Took less than 5 minutes and the pedal firmed right up. There was definitely air in the line. I couldn't believe how bad it was. My rear brake was nearly useless and I've been riding it like that for a while now.
I'm a happy camper now! Cost me all of $5 for the brake fluid and $30 for a vacuum pump with gauge from Autozone which will come in handy for a great many jobs I'm sure.
Now I need to change the fluid in the front brakes.