GPS decoding is less computationally difficult than you seem to think, and in any case, in phones it’s done by a hardware module. The Garmin Geko handheld GPS was made in 2003 and ran on two AAA cells for 12 hours or something like that. Today’s GPS’s fit inside wristwatches and use even less power. It’s just not that big a deal. The cpu load of mapping applications on phones is dealing with the maps, computing driving directions, etc.
I wouldn’t worry about map updates by internet. The roads don’t change that often. You can update from a USB-connected computer once a year or so and be fine.
The other stuff doesn’t sound too bad, though idk why you want a phone for the purpose. If the GPS is for road navigation you can get an old dedicated unit that runs on 12 volts do you don’t have to mess with batteries. Those were nicer than phones in some ways. I still have a couple of them kicking around.
I just meant the amount of computation required of a gps receiver isn’t huge by today’s standards. Remember that gps was designed in the 1970s for use with the technology of that era. Today’s stuff is 1000s of times faster.