1. You will not be submitting a 3+ month charge for reimbursement, you will be submitting a new one. The "posting date" on your CC will show that should someone challenge you. Pretty basic accounting that you can't submit for reimbursement what hasn't been charged to you.
2. Disputing a CC charge for a legitimately owed debt is a big no-no. The property knows that. And, it's likely that the Manager could actually care less if the dispute is sustained. It's easier to explain than explaining why. And, the CC dispute isn't the end of it. Marriott will simply send the invoice of to a collection agency. That can be unpleasant and have long-term bad consequences.
3. If you ever stay at this property again, you have made yourself a doormat. Don't.