We're both multiple generations away from ever having actually experienced and used violence, so neither of us has a real view of what this looks like...
But just looking at this on first principles: Is sticking a couple of heads on pikes REALLY that big a deal if the outcome is you Literally Rule New York?
> full of people who would have to be removed
Well no, you wouldn't do that, you basically can't because the entire New York economy depends on them. What you could do is:
1. Make landlords liable for the criminality of their tenants - so practically speaking every renter has to get insurance against being a thug.
2. Designate "nice" areas of the city which require a certain amount of bond in order to enter. Workplaces can insure their employees, tourists can apply for insurance before visiting.
3. Do not allow protests. Arrest protesters, go after their landlords / insurance for compensation. If they start throwing Molotov cocktails, respond with live fire.
You setup a system like this and things will start cleaning themselves out over time...