End of the lease for tenant, second smartest thing to do?

[Robert Lei]

I am sure I am going to get a lecture about being "soft-hearted" and not firm enough with my tenants, but hear me out. As I am typing this narrative out, I've realized there's a lot, so here is everything in sequential bullet points:

*Bought a property and inherited tenants

*Tenant's lease is ending, September 1st being the last day

*Appropriate nonrenewal notifications were sent to her via email and text on August 2nd

*She knew I didn't have plans of renewing based on our face to face conversations

*She hasn't paid August's rent yet

*I called about August's rent, she said she "need to save the money to apply towards the next place, since local rent has increased"

*I explained she still owes rent, and her security deposit can't be used as rent

*She gives me a sob story (3 kids, new school year, low paying job [all true]), wants to sign on for another year

*I cave and suggest to her a different option: best I can offer is m2m, but will have to sign a new lease(I was thinking with stricter language, possible rent increase)

*She is concerned with how long the m2m would extend for, to which I have no answer

I know there are red flags, but I am only considering the m2m because:

1. I am currently TDY (military) and won't be back till mid September

2. She has paid all her rent up to this point, so I know I will get the money

3. The cost of eviction is too much and takes too long considering I will get paid the rent

4. My plan is to install carpet and a washer/dryer in the unit after she leaves. I can't start the reno until I come back in September, so the unit would sit empty for a month or so

5. She hasn't really caused any issues leading up to this point, so I am not so quick to kick her out

As far as I am concerned, I feel like I have the upper hand because I am lenient on the lease, but not to the point where it is hurting my business. Obviously the smartest thing here is to show her the curb, but what's the next best thing I can do? If she leaves by September, I won't be around to make she leaves quietly. Also, I can't start the renovation process and finding new tenants, which will cut into my bottom line.

tl;dr: inherited tenant can't move out due to some finance issues, but pays rent. besides kicking her out, how can I help her and help myself?