Judging from the states on your map, I'm guessing that you're looking at flying in the south. In the winter you'll still have icing concerns, but you'll probably be fine most of the year. If you have commercial as a viable (albeit undesirable) backup option, then that also helps
You'll end up wanting as much speed as you can get. With bad headwinds, the westbound journey can be painfully slow in a number of planes. But that said, if your business gives you the flexibility of +/- 1 day then that might be enough to avoid that most of the time. Anything slower than about 150 kts on average will get old fast. A Comanche 250/260 seems like a good option, so does the Bonanza. The Turbo Twin Comanche option that Kent will tell you all about would also be good, as would a Seneca II. Another option I would look at that I think is under appreciated is the Travel Air. A friend of mine has one - it's a very nice airplane, and has similar performance to a Twin Comanche (as far as I can tell) with better interior space. It's pretty much a 55 Baron with Lycoming O/IO-360s instead of the Continental IO-470s.
Depending on what your wallet allows, an Aztec/Baron/310 also produces a good option. The Baron might be a good one for you, giving you both good speed, acceptable room for you and your family of four, and you can get them with de-ice. An Aztec is real truck, but it sounds that for your standard mission, a Baron or 310 would still give you sufficient room and useful load without the speed penalty. The Aztec is slower than the Baron or 310, but it hauls more and is a tank.
To give you some numbers, I run 155 KTAS at 20-22 gph combined in the Aztec. My friend's Travel Air runs 155 KTAS at 15-16 gph combined. Others here can tell you their numbers.
I would suggest is that you try to get a plane with de-ice, even if you don't intend on using it. The reason for that is that is twofold. First off, if you buy a plane you'll likely want to buy one that you won't outgrow. Even if you aren't going to use the de-ice whatsoever for a few years, then that means in a few years it's there and you don't have to sell the plane and buy one that has it installed. The second is in case you get into it inadvertently. Of course, that pretty much puts you into the twin market, which you may or may not want to be in. The insurance and MX is higher, but I find for long XCs it's very nice to have. If nothing else you have little advantages, like when alternator or vacuum pump goes out you're not dead in the water.
Where do you live exactly? If I'm ever flying through your area I'll take you up in the Aztec. You might fall in love.