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I have a GPSMAP 64s and an eTrex 20. They both have GLONASS and work better in areas with bad reception which include slot canyons than a unit with GPS alone. I don't notice the 64 being any better or worse than the eTrex in the same location. There are differences in the two units but I don't think accuracy is one of them.
The lack of expandable on an eTrex is only true for the 10. If you are only looking to get location off the GPS like I was thinking memory is not a problem. If you are looking to have maps on the GPS the eTrex 20 and 30 have expandable memory with micro sd cardFailing all that, I was looking at eTrex a few days ago, as Boyd mentioned. My only concerns with that one are size and the lack of expandable memory. I don't know how big a deal that last point is, but I've heard that it's going to be tough for me to get enough coverage on that thing.
@Tim Will an Edge 20 or Forerunner 10 give you Latitude - Longitude or better yet UTM? If so they would be good as They are small and light
An eTrex would also be good. They use AA batteries so power is not a problem. The eTrex 10 is cheep and would work for this use.
For what the OP is asking any GPS that gives Lat - Lon or better yet UTM would work. After getting the numbers you could transfer them to your map. I would work with it ahead of time to make sure you know how to transfer the position to the map.
I have done off trail backpacks of 2 weeks plus. We use a map and compass to navigate and once or twice a day power on the GPS to check that we are where we think we are. This way the batteries will last for a long time.