Make sure to take frequent (like hourly) pit stops so you don't get crampy. And bring a hot water bottle or some kind of portable heating pad for your back, hips, pelvis, etc because you're going to hurt...and walk a lil bit each time you stop so your legs don't swell too bad with all the sitting.
Not just route the hospitals also look for the ones that deliever babies because some hospitals don't
It's going to be a very uncomfortable car ride. I wouldn't put that stress on you and the baby so close to your due date. I traveled at 20 weeks and 27 weeks. Each ride was 7-12 hours because we had to stop so much, I was hurting from sitting/laying so long. I had spotting and bleeding from it. Never doing that again. Have a back-up plan and route all the hospitals along your route if you decide to go. Good luck.