It also says that "The new loan amount can be no more than the actual documented amount of the borrower's initial investment in purchasing the property plus the financing of closing costs, prepaid fees, and points on the new mortgage loan (subject to the maximum LTV, CLTV, and HCLTV ratios for the cash-out transaction based on the current appraised value)."  

Is the “total cost” of the loan the “prepaid items” + “closing costs”?

Please tell me you are not advocating for a cash-basis investor who almost certainly has a lease that crosses calendar year end, to accept prepaid rent for multiple months.

The 1 exception to this rule is called Delayed Financing - if you purchased the property without securing a mortgage, you can do a cash out refinance within 6 months and the loan amount will be capped at the purchase price + closing costs and prepaids. 

This is considered pre-paid rent, and it can not be disbursed to you for future months.  

Prepaid Legal maybe?

With the delayed financing I was able to get a loan for $73.6K (includes rolling in closing costs, prepaids, etc.) with conventional financing @ 30 year, 4.5%.I will collect ~$3,800 in rent before my first payment.

There are valid reasons to choose any of the above options, depending on how long you plan to have the loan for.Now $4500 to $6300 sounds really high, which leads me to believe that either you would be paying points, that those include escrows and prepaids, or that you are getting hosed. 

Specifically the security deposit and prepaid rent portion.The security deposit, including any prepaid rent cannot exceed 1.5 times the rental amount.

You got about $4800 in prepaid S and state taxes, E, F, G and your lender has no control over that.