As a private lender in Tampa FL, I structure my new construction loans where the property must be owned by the builder, and then construction costs are provided in arrears, meaning you have to put your money to work in the project first and then I reimburse you. 

For instance, most hard money lenders, like myself, provide rehab funds in draws on reimbursements.

(Invoices sent in to allow the insurance company to reimburse us for our expense) It’s been five months since our final invoice, and yesterday, our contractor called saying they came across some invoices that they had missed that needed to be paid.

You can sue the HOA and get reimbursement later. 

You'll have to pay for some of the work up front, then get reimbursed as its completed.

I'm leaning towards a HML and then funding the Rehab work out of my own pocket on the front end ( Material costs only ), but still having the cost of the materials financed into the HML on the front end of the deal and getting reimbursed the costs for materials when I refinance into a 30 year fix.

Would the oil heat fit into the GRM calc if it's kind of a "reimbursement type situation" where landlord pays and then tenants reimburse?

The sellers get the property sold, and if for some reason you fail to close, they get all the repairs done for free (they're reimbursed the $20K they spent), and will likely make an extra $20K on their sale.

Everyone is happy.Day of closing, final HUD sent to underwriter and she decides I am not allowed to be reimbursed for the expenses I came out of pocket for, and had a signed addendum stating I would be reimbursed. 

There’s nothing to really encourage them to pay at all with a moratorium in place, even after an owner is reimbursed.