There's a strong leaning towards the eTrexes on YACF, because of the waterproof and AA battery factors, so the eTrex 10 is probably your starting point. A low-end Edge might do what you need, though, if you're happy with an internal rechargeable. Otherwise there are the Bryton units, though I hear the software's a bit iffy, and don't know anyone who actually uses one.
I assume you've dismissed the smartphone-in-an-appropriate-bracket approach? Not something I'm keen on myself on account of the power issues, but might be a reasonable approach for shorter rides...
The eTrex H cutting out is a known fault that may be repairable: Try different flavour batteries (some do rattle about in the compartment), and if that doesn't help take it apart and solder bodge-wire between the battery compartment contacts and the PCB, maybe adding an electrolytic cap for good measure. It's a spring-vs-PCB-pad interface that wears out with prolonged vibration. Re-fitting the outer rubber band can be achieved with extra-strong carpet tape and a scalpel.