@QueueCT--I have been using a Garmin etrex Vista HCx for several years for randonnuering events. It has been discontinued but is still fully supported by Garmin. The Vista meets all/most of your requirements for a GPS unit. It is available on Amazon for under $200. It is waterproof since it was originally intended for marine use although it will not float like the Garmin 76CSx. It comes with a plastic Garmin handlebar mount, but I would recommend using a steel U-bolt type mount available from RAM mounts. The RAM mount is more secure and can be oriented in a variety of positions. The Vista can be powered by two NiMH, lithium, or alkaline AA batteries. Run time is about 16-22 hours depending on battery type, usage of the back light, compass, etc. I have been very satisfied with it's navigating capabilities when I load a route that I have created from a cue sheet. To use the Vista for this purpose, you would need to insert a 2 or 4 gig microSD card into the slot in the Vista to increase the available memory. You would also purchase Garmin's map set DVD "City Navigator North America" which is available on Amazon or direct from Garmin for under $100. You then load "City Navigator" onto Garmin's mapping software, "Mapsource" which is included with the GPS purchase and create your route. Then just transfer the route, waypoints, and map set(s) from your computer to the Vista with the cable that is included with the Vista purchase. I do not have much experience with loading and navigating already created routes from other sources, but I think if the routes are created in or converted to a gpx format the Vista would be able to navigate them.

@dcrowell--I am curious as to why your Vista won't follow the routes that you have programmed. My Vista is generally spot on in navigating routes that I have created from cue sheets. I have used it successfully on many randonneuring events including 1000 and 1200Ks. I find the rare deviations from the intended route are generally due to errors that I made in programming the route. Perhaps the problem you are encountering with navigation involves the options you chose in the initial configuration of the routing sub-menu.