Anyone moved cross-country with a cat? Advice greatly appreciated!

My husband and I are moving across the US in about a month (about a 12-13 hour drive, not including stops for food and gas). I'm a moving pro, but I've never had to move with a cat. I'm starting to get anxious about getting her there safely and without traumatizing her.

A little background on Miss Kitty - she's a 6-year-old shelter kitty. We got her when she was 4 (she'd been a stray for a while but was microchipped so was clearly previously someone's cat), and she's been very healthy and normal weight ever since. She's the most attached cat I've ever had though... she loves to be near me all the time and trails me around the house like a dog. She does have an anxious streak, but it's not extreme. She does NOT like cars... I've tried to acclimate her to the car in anticipation of this move, and she just howls and cries when it's turned on. After about 30 minutes I stopped wasting gas and brought her back inside. It made me sad, so I didn't try again... but I'm willing to stick with it if people have ideas how to make it work.

Does anyone have any suggestions for making this as pain free for both of us as possible? I was thinking of getting her a cage made for medium sized dogs with a litter box and her bed inside, but leaving it open so she could come out and sit with me in the back seat (my husband driving). I've also considered drugging her, as I'm worried she might really stress out and 12 hours is a long time. Any and all thoughts and experiences appreciated!

Here is the little Miss warming her paws this winter: Oh Hai. She says thank you!

tl;dr - Help me drive my cat across the country without traumatizing her for life.