Would you like to know how I would fix the problem?
I would. Please proceed...
Well, I've pointed out three main problems:
1) Public property means it's their road too.
2) We're currently punishing blood content instead of impairment
3) We're treating people who have harmed no one like criminals
The first one is as simple as defining the problem. Public property is the problem, so private property is the solution. Privately owned roads would allow the owners to set the rules for people who drive on them. There could, theoretically be roads which allowed people to drive impaired (which would likely be deathtraps - Darwin at work) and roads which did not allow people to drive impaired. People could then decide how much risk they wanted to take, rather than being forced into a one-size fits all risk plan.
The answer to the second one follows from the first. Private road owners who prohibit impairment would probably like to keep their insurance rates down, as well as make it as pleasant as possible to use their roads, so as to increase their customers. To this end, they would likely want to make sure that impaired drivers don't cause accidents. The surest way, of course, is to remove all the impaired drivers from the road. With the option of taking the other road open to them, fewer will drive on the road that prohibits their behavior, but for those that do, an arbitrary blood alcohol content is a poor indicator of impairment, especially for the other forms of impairment I've mentioned. Therefore, impairment testing, such as the "road sobriety test" and various other more high-tech means, would likely replace the breathalyser or blood tests as measures of impairment. Being private property, the road owners can set punishment for driving impaired, but being business owners, would likely limit this to refusal of service (ie banning from that road).
And finally, by holding all accidents to the same standard, regardless of why the responsible party caused them, and requiring that they pay restitution, you hold the driver responsible for their actions. This, I think, will greatly reduce all forms of irresponsible driving, from drunkenness to road rage. True, restitution does not return a lost loved one, but neither will paying for caging a man, and at least he's supporting you in your time of need, instead of the other way around.
My solution would be along the lines of subsidizing the aformentioned micro-nations enough to keep them operational and thus, hopefully, help keep the BFL types from contaminating ours.
You're assuming they wouldn't end up subsidizing the welfare states to keep the leeches from contaminating them.