Also, needs oil remediation.

Any possibility of getting a narrower range of the cost of remediation? 

Would a larger hot water heater remedy hot water running out because of usage?

She was not given an opportunity to remedy.

Our rights and remedies under this Lease are cumulative; the use of one or more shall not exclude or waive our right to other remedies... 

Do you have any recommendations on how to remedy the situation?

If not, I would still recommend going ahead with a professional cleaning company that has experience with mold remediation (make sure they send before and after pictures as well), if you really wanted you could give a small credit to the tenant to make them happy as well but 100% not required. 

Once we were aware of this and the owner refused to properly remedy the issue we had to cut the property, we actually cut the client and his 6 other listings.

We were told we have mold in our basement and got 1 quote for mold remediation and it came back at $5,500.

@David Kirkpatrick hmmm... here are the problems I see with this scenario (and that you need to remedy).