From Show Low, AZ to the Hospital, there is one J1772 outlet at:
Quality Inn, 458 E White Mountain Blvd., Pinetop, AZ 85935
https://api.plugshare.com/view/location/79860
I would consider this an "emergency" stop only.
If the hospital will let you charge, obviously any LEAF can do the job. Yes, it's great to hedge your bets with a "better" LEAF with faster charging, bigger battery, more efficient cabin heater, etc, but it's just NOT required to do this drive.
One thing I would require is that a dedicated charging spot with 240 volt service be written into the contract. They can EASILY do that with a dedicated 120 volt outlet, simply by using the existing wiring. Just swap the single pole 15 or 20 amp circuit breaker to a 2 pole 15 or 20 amp circuit breaker (this normally just pop in, and typically cost $10). Then, just move the white "neutral" wire to Line 2 in the breaker box. Wrap some black tape around the white wire at each end to indicate that it is now a 120 volt wire, and not a neutral.
Then, pop in a dedicated 240 wall outlet like an NEMA L6-15 (for a locking 15 amp circuit) or a NEMA L6-20R (for a locking 20 amp circuit).
Again, in writing, with 240 volts. It's cheap and easy for them to do (again, assuming a 120 volt dedicated 15 or 20 amps outlet is already waiting for you).
Then, I would LEASE a LEAF. The deal I got in California with zero negotiating was:
$33k for a 2017 LEAF-S with 30kWh battery and fast charging (you actually don't need the fast charging, but it won't hurt either)
$14k discount ($7500 IRS tax credit to Nissan plus $6500 discount from Nissan)
$10k total cost of LEAF for 36 months (about $277 per month)
$9.1k residual (what you are going to pay for the car to buy it in 3 years)
$0 down with good credit
$2500 California state rebate check that you won't get
If you can't find this locally in Phoenix, ship one from California for $600-$800 typically.
This car will make the round trip at the speeds you outlined without charging at work much of the time, except the coldest days with the heater blasting. You'll want the backup J1772 plug at Quality Inn for days when it looks close (that's the ONLY place the the 6.6kW - 27amp onboard charger is an advantage over the regular 3.3kW - 16 amp charger).
But, I would count on charging at home with 240 volts. Don't play games with a NEMA 5-15R normal household outlet for commercial duty work... get a 240 volt dedicated outlet at home, preferably a NEMA L6-20R that won't accidentally become unplugged or be accidentally only partially plugged in. No fires and no burnt up plug or outlet.
The last piece to the puzzle is either buying a dedicated 12 amp or 16 amp (depending on whether you have 15 amp or 20 amp outlets on BOTH ends... home and work) charge cable that can either handle 120-240 volts, or just 240 volts. You can keep the stock cable as a spare (it's 120 volts / 12 amps), or pay about $300 to have it modified by EVSEupgrade for 100-240 volt capability at 12 amps. I would specify a NEMA L6-15P or L6-20P as appropriate for your outlets at home/work. Obviously, that will prevent needing adaptors.
That's it!
1) Get dedicated 240 volt outlets at both work and home. Get it in writing at work ($200 max for home outlet)
2) Get a 240 volt portable charge cable or modify your stock cable ($300-$900)
3) Pay less than $300 per month ($10k over 3 years) to lease a new car for 3 years, then $9.1k to buy it forever after 3 years
4) Make friends at Quality Inn hotel, should you ever need them as a backup