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I have a Garmin Edge 305 which I like and have had for a number of years. It is also starting to suffer from "switching itself off" problem most develop after a while.
I would really like a GPS which has the cycling and fitness features of the Edge but also displays your actual position in OS grid format for use with paper maps.
Does such a thing exist?
Not seen one. If you have a Smartphone, then the options are there.
Edge 500 can show you OS grid, but unfotunately not as an option on the main screen. It's in the satellites menu so easy enough to find.
My Edge 205 died and was replaced by a 605; OS grid refs and colour OpenStreetmap mapping made me a very happy person. It's not OS mapping, but it has contours and as much map detail as you or somebody else has put on OSM.