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.

No idea what she's talking about. Also higgledy-piggledy? LOL. Toyger, you pick some interesting material to learn English mate, but yeah the whole sentence is kind of a mess and doesn't really make sense.