I also think you will have to really consider if you need pressurization. If you stick with this requirement, this massively limits choices.
Limits yes, massively limits not so much. Once you get into the cabin class realm it almost gets harder to find planes without pressurization. Given his desire for 4 people and light load of luggage, the pressurized versions would be the PA46, Cessna 340, arguably Piper P-Navajo... he could get a Duke! Or any of the various single engine turboprops or lower "entry level" twin turboprops, all of which are pressurized (other than the Caravan, which would not fit the mission at all, and a couple of oddball freighters).
For the non-pressurized planes that meet his criteria there's the Navajo, Cessna 335/401/402 (none of which are in significant supply), PA-46 Matrix, then a few oddball planes that I wouldn't recommend to someone looking for a reliable plane receiving that level of use. It's actually harder to find a good 335/401/402 than a 340.
If the cabin class and airstair door are removed from the requirements, then yes, it does significantly open up the requirements. But there's a reason why planes that fly passengers that much are generally cabin class - eventually it gets old for the people in back to be in back of a 310. But a Navajo would be a good, comfortable, and reliable option if pressurization wasn't mandatory.
Personally, I think the mission would be better suited to a turboprop (and a short body MU-2 would be a perfect fit!) as I'm skeptical that any turbocharged piston plane (except maybe a Navajo) will fly between inspections without significant issues popping up semi-regularly. But the people footing the bill may not want to make that jump at first.
I would also want pressurization if I was based where Billy lives given the other requirements. MEAs and weather, especially if he flies north at all, will be a whole lot easier to deal with with pressurization. Turbos without pressurization limit the gains you get from that expense of turbochargers.