You have the same control with an auto--just hold it down a gear if it hunts.
Climbing a hill is not a low-rpm torque event. It's a horsepower event. If you need 150hp to climb a grade at the speed you would like to climb it--a 300-6 will have the pedal to the floor at its maximum rpm and a 460 will be loafing up at 2/3 throttle. In Colorado where the hills are mountains and the sheep are nervous, I wouldn't want a 300. I think you lose 3% of your rated power per 1,000' because the air is getting thinner. If you are at 5,000' in Colorado, that 150hp 300 is making only 125hp. The 460 can still make the power.
I would, of course, suggest a turbodiesel which loses no power in the hills, but your budget was only $2k. So get the biggest motor you can get. A 460 is 65% larger than a 300 and is a more efficient motor as well.