Refinance a private mortgage without seasoning at 100% LTC

I'm acquiring a property at 65% of ARV using a private mortgage (secured against the property) and then want to immediately refinance the property using a conventional mortgage through a normal bank to pay off the private mortgage. Only issue is that I'm being told I can only get a refinance loan for 80% of the purchase price. Because my private mortgage is for 100% of my acquisitions cost, this means I have to leave 20% in the deal. Is there some way around this??