We did a similar mission for years in our 310R (naturally aspirated), 800 miles from Phoenix to Rapid City, SD. Actually, we still do it. So many trips across the Rockies, plus we've done Oshkosh and other places really far east of where we live. It's been a great airplane for it but as the frequency increased we've decided to move up, plus pressurization when you're in the Rockies once a week will be really nice. For the 3.5 years we've had it it has been a really great, solid airplane and I'm so glad to have been able to own it. The dog was a big factor in our decision to move up because of the pressurization.
So, long story short. The 310R is a great airplane for your mission. Just a personal opinion though, from someone who has been there and done that, and still doing it (until ours sells)