Hard on the problem not on the tenant. Meaning be cordial to them but explain you can not have a property/tenant that is not paying. I used to hate these type of issues because it really creates a scenario where you have to look in the mirror and figure out how you are going to handle it. But now I just follow the same procedure regardless of the tenant or situation.
Keep eviction process going as that is your procedure when you do not receive rent. Already a pretty difficult tenant for you why try to keep them in?
or there is the magical and ever so effect cash for keys - you will give them x dollars if out by z date and the property is in good condition. Even if negotiating this arrangement the eviction process does not stop.
I would not recommend handling an eviction on your own, especially in this situation too much recourse for the minimal difference in price.
Lastly - if you don't collect the late fees now, when will you?