Looks like you are reading a British author. Stop-start we use for something starting, stopping then starting again and so on, intermitten. Eg he has had a stop-start career. Mostly, I saw it in sport articles.
I don’t know a broader context but as higgledly-piggledy ( topsy-turvy is another one for you ;) means, chaotic, it has to do with their often interrupted, chaotic, disorganised renovation.