Traveling with four aboard, will be difficult with any Mooney. You run out of space pretty quickly. And you need enough power to do it safely in the higher density altitudes that Denver is known for.
People focus on fuel burn, and compromise the aircraft selection to fit that choice. You really need to focus on the mission, and the fuel burn will be what it is. It's not as big of a number as you might think.
You're going to need more than 200 HP, or turbocharging, or both, to fly the West safely, fully loaded. A K model might work, but space will be an issue every time. An Ovation would be OK but they are expensive. And the cabin is still not very big for a four person vacation machine.
25 years ago, my travel requirements with three kids pushed me into a six place airplane, and due to the high costs of six place singles, I ended up in a Piper Apache. And also a Twin Comanche, and now an Aztec. But the lower capital costs more than offset the higher fuel costs. The huge cabin made everyone happy too. A happy family means more airplane trips for the happy pilot too. Don't buy a plane that the family hates to travel in.
The same goes for the speed. 5.7 hours in a comfortable plane is better than 4.7 hours in cramped conditions. And one hour is all the difference there is on an 800 mile trip at 140 knots, versus 170 knots. But it costs a whole lot more to go 170 knots.
You might consider a Turbo Lance. Plenty of room, plenty of power, the speed you want, and there are some in the $130-150K range that have good engines but may need some avionics updates.