Tenant who is unable to vacate? Start eviction process?

[Nadir M.]

I currently have an issue with a tenant that I have been trying to remove since May (that's when their lease was over). Due to the moratoriums, they are currently month-to-month. My PM sent the 30 day notice on June 30th. Today, I was made aware that she was unsuccessful finding a new place due to her credit score. She stated that she filled out several application with no luck. She said there is a apartment complex that may take her because they do not make their decision based on credit score alone. She's not a good tenant. She doesn't care about the property nor does she care about maintaining it. I've tried to maintain some of the maintenance out of my own pocket. I do plan on taking that portion from her deposit. My PM told her that if she does not find a place by end of July that we will start the eviction process. This worried her a lot as it should have. She texted me and told me that she needs to stay until end of August in hopes that this new complex will take her. She said she is willing to pay extra to stay. My issue is this: I need my place back so I can clean it up and make it look presentable for the appraiser because I want to cash out refi. This was my goal at the beginning of Spring. If no one is willing to take her now, I do not see that changing in the next month. I do want to start the eviction process and have her out by end of August for sure (contingent on her not finding a new place by the end of this month). If they do not accept her and I start the eviction process, I'm worried she'll trash my place even more. So do I have her stay another month, pay the increase, and help her find a place (we have gave her some options already) or do I start the eviction process and hope that the damages are reversible? What's the best strategy or approach? My PM suggests that she stays and pays without evicting her because evicting isn't free. I just do not see that as a viable option. How do I get my property back under my possession? 

Thank you,