I've known a few operators using 310s from rough strips, none had particular trouble with the landing gear.
I know you asked about the 310, but at a quick glance, it doesn't sound like that would be a good choice for your mission. You didn't say how far/ where your typical trip will be...short hops, or long travelling trips? If short hops are the norm, I'd sure try to figure how to stay away from the turbocharged engines, they don't like 10-minute legs very well. You mentioned hot weather, but unless you're also at higher-elevation fields, turbos would not be worth the etxra fuss.
the C206 sure sounds like a better choice, but if you need the second engine, how about considering a BN Islander?