Tell me you didn't read any of the thread without telling me..
Because if OP dumps the car on the road, she's broken the law, she's dumped car - you can't actually dump cars on public roads any more than you can dump litter or kitchen sinks.
Regardless of what the cars owner may or may not do about it, the police could take action, she could be charged with theft, criminal damage, abandoning a vehicle.
And 'just tow it' - that assumes OP owns a tow vehicle, I suspect they do not.
So that means calling up a tow company and asking them to take a car they have no proof belongs to the OP (because it doesn't), and commit an illegal act (dump it on a public road). That would almost certainly void their insurance, they won't do it. She can't lie and say it is her vehicle as she has neither the keys nor the paperwork.
So your solution is not just impractical, it is illegal and impossible.
@Avacadosprinkles - send a letter before action, its free, it simply sets out what the situation is, what will or may, be happening, and in what time frame.
Then you've started the ball rolling and have time to find proper legal assistance IF it is necessary but often an LBA will make things move, if its set out properly (and much as it pains me to admit it, Chat GPT or googles AI will do that for you easily).