@Andrew Katz
In this situation, you can either (a) continue dealing with the pain of having your tenants that pay late and violate your lease terms or (b) deal with the pain of turnover but the prospect of getting better tenants.
The first option will give you continuous headaches with a certain likelihood that the behavior may get worse (not paying at all and more damage). The second option at least gives you a chance at a fresh start with a new tenant.
Of course, a new tenant is an unknown and there's no guarantee they will be better. Were you thorough with your tenant screening for your current tenants?
If you hate the process of placing tenants, it may be worth it to hire a property manager to handle tenant placement for you.
I think finding a new tenant is a better long term strategy if you're confident you can find a higher quality tenant that will cause you fewer headaches. In the short term, it will be more painful though.
Personally, I'm not a fan of enabling bad tenant behavior and in life you get what you tolerate. They aren't going to magically improve and start abiding by the lease terms but I think there is definitely a possibility that the situation gets worse.