Nice theory but I haven’t seen any correlation in NJ. Can you point to reported violations or any other stat that shows correlation to the counties now experiencing faster doubling? The only correlation I see is a much later start date which clearly speaks to the virus having run its course in the counties with 30 days plus doubling time.
I don't like the doubling stat as a barometer, because it is only a good stat if conditions stay the same through the life of the case study. By all accounts, North and Central Jersey started taking social distancing very seriously from mid-to-late March, after the first spike in reported cases, which completely alters the trajectory of the spread. I don't have social distancing stats for either part of the state, and they wouldn't be reliable even if I did. I know enough about South Jersey to know it is highly likely social distancing isn't being taken seriously and that LE is under-reporting it, if they're reporting it at all.
In the same vein, to say South Jersey has been complying with social distancing regs and they are
still experiencing a surge means that this virus is spread in ways we previously hadn't considered, making this scarier than it has been until now.