A mixed system which starts with changing the most socially egregious examples is probably the only politically viable transition; lots of people fear disruption, and it takes time and proving to them that the changes are beneficial.
I'd suggest beginning with something like Corbyn's Labor had proposed; if a capitalist business is sold or fails, the workers are given first right of refusal and a govt loan is given for them to purchase as a worker cooperative.
Not everything has to be "the replacement for cars". I hope diversification is the "death by a thousand cuts" to cars, where everyone has an option that best accommodates their situation.