Any of the Garmin GPS units will store a track log that you can use. I have a Garmin Legend and after a long ride, I upload the track to motionbased.com (I use the free subscription) which will plot the track as well as provide various statistics. For the Year-Rounder, I copy the URL to the uploaded data and submit that to UMCA. Works like a champ and much easier than mailing in receipts.
The Legend, as well as any of the general purpose GPS units from Garmin, use replaceable AA batteries. I find that one set of Alkaline batteries is good for up to 400Km, depending on how much I use the backlight. But, even if the batteries do run low during a ride, it's trivial to replace them.