I think north or into a core on dirt is still valid escape if there is no better option (dirt in all directions and all wet, or paved north, or another route is definitely in path of a tornado that is close by). It would absolutely be better to be cored than trying to outrun a tornado if you can get out of the path with certainty, even if you got stuck but made it out of major danger. Traction must be factored into escape routes of course. The three hour rain product some radar apps have is invaluable; I can usually tell when a road will be dry, wet, or nightmare with pretty decent accuracy, if it is not obvious from having a huge core go over the road. Another factor on escape routes out on the plains, which maybe you have encountered out east as well, is random closed roads with no warning. This has happened to me three times while using my escape route before (I very rarely need to use one since I don't usually chase that close). In one case I was cored and learned to stay back further from volatile situations, and the others were closer escapes from hail and a not yet producing tornadic hook.
AWD has worked great for me for 10 years of chasing, including sliding like a boat through Nebraska clay as I chased a tornado from a safe distance behind. I am sure in certain scenarios true 4WD is better, but once the roads are a certain level of bad, only monstrous mud tires and torque are getting anywhere fast. A lot of the modern AWD are incredible at traction control (Honda, Subaru, etc) by independent electronic adjustment to torque on each wheel, including mud and sand modes that behave more like 4WD. 4WD usually comes with less fuel efficient vehicles, so I am one for the slight less traction in extreme scenarios in exchange for comfort and fuel economy and great on pavement manners. Subaru of just about any model would be a great choice as would a lot of the modern major reliable brands.
For finding shelter, I meant for your car with you in it unless you are about to get hit by truly massive hail or tornado. While some may not care, I don't like hail damage or windshield loss, so I will find shelter even from medium hail under a car wash or gas station overhang, or just stay out of the situation in the first place. I imagine squall lines move at similar speeds everywhere, but it seems most of the extremely fast ones I have had to move to shelter for were in KS or NE, which often form behind you if you chase a leading supercell. I think your existing rules about avoiding squall lines are very smart.
If you are aware of a gust front or RFD, it is not surprising and can usually be dealt with, not without sometimes a hail, dust, or other risk. So in the aspect of expecting it, you can be 'ready'.