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Hello and thanks for your finance question.
I think it totally unreasonable to expect a bank to lend you money for security for a $7MM LOC. The reason they bank wants you to put up $500K is so that you have some "skin in the game" and the bank is not on the hook for a $7MM loss entirely. NO, the will not give you the $7MM with them having 100% of the risk!
I know this is not what you wanted to hear, but you cannot borrow the money for this type of transaction (the down payment portion). You can get another equity partner or someone from the outside who can lend you some money, but you are trying to leverage a leveraged transaction. No lender would like to see that.
An equity partner can bring cash to the table so that you can leverage the commodity transaction using the Bank LOC.