Absent any additional activity I would not offer above asking and simply submit what you feel is a good fair offer and wait on a counter or acceptance. 

Therefore I think you will either need to be loose with your tenant base, accepting higher risk tenants, or expect more vacancy.  

I don't see a way that the cleaner can "accept" a cleaning job where it will show me that they can do it, am I missing something there?

I believe that through section-8 the tenants still have to apply, and as the landlord you can choose to either accept or deny their application.

I just got my offer accepted.

I sent them a text and reminded them that our lease states they need to pay on apartments.com and I will not be accepting payments any other way this time.

You don't want her to leave and these others not to or if you have to move her out have them rush into court and say they are not named and therefor they can stay.If you accept any money be sure you put on the receipt that it is for use and occupancy ONLY and not renewing the lease.

Ask your real Contractor if he will accept the responsability and warrenty all the work, just sounds to me that you are looking to have no responsability and to pass the buck.

My insurance did accept my claim but I have a 1% deductible (around $3500). 3) Water service was turned on and off around 10:30 am per Water Authority.

I specified single family because they are a dime a dozen, and in any MLS there should be good diamonds in the rough out there outside the mainstream of shiny objects being bid up above asking by desperate buyers (sometimes mispitched in listing to the wrong category by an idiot listing agent, which a good buyer agent can find and offer on as the only offer they've gotten in the past month!)