I believe a iPad will charge albeit so slowly that a screen warning may pop up stating that its not charging.
Saying that, Apple Macbook Airs, iPad and iPad Mini boast a 10 hour battery life which is pretty much up there as far as what your looking goes.
Add in a high capacity battery and you extend this.
I've got a Macbook air I've just gotten to accept a battery via a cable from Ebay.
These:
ebay.com.au/itm/T-Head-Power-Bank-Male-Connector-DC-MagSafe-2-Cable-For-Apple-Macbook-Air-Pro-/111239821478
ebay.com.au/itm/23000mAh-Solar-Backup-Power-Bank-Charger-External-Battery-For-PC-iPhone-iPad-/371052999904

Thats the guy I got my cable from but the guy I got my same battery from has none listed currently.
Being Chinese you can't believe the mAh figure but it appears thus far offer plenty of oomph and thus bang for buck.
I'd also ignore the solar part of the equation as I believe it would take days to charge although I've not really tried.
For me its a stop gap measure should I need it which is unlikely as my bicycle and extra wheel trailer both have Son28 dynohubs which keep on top of everything enough for my use. (so far my Garmin and iPhone successfully)
I'm yet to explore trying to jury rig my E-werk to try to get a slow trickle charge into the battery.

Before anyone suggests I've insulted non Mac users - far from my intention.
There is bound to be alternatives that equal or better Macs claimed 10 hrs battery life.
I'm not stating Mac is best but merely that its up there with the best I've personally found.
Plenty of room there hopefully for someone to not feel threatened by my view that Macs are OK.
I'm merely stating an opinion that Mac products might be worth a recommendation for the OP as being close as the competition (as far as I'm aware), to the OP's parameters.
OP might have to look at secondhand though to come in within the $500 budget.
Also be aware that theres talk of iPads needing to be cellular enabled for the gps to work.

Hope some of the waffle is worthy of thought or further discussion.
If not, C'est La Vie.