Private lender for down payment

[Blake Cross]

I'm looking for help or advice. My wife and I have 4 short-term rentals in Gatlinburg, TN and are under contract on two more. We have the cash for a 20% down payment for the first one, and initially intended to sell one of our others to 1031 exchange into the second one. The second one will not close until late June due to it being currently under construction. For this reason, we're trying to use this time to be creative to figure out how to keep all of them. We'd like to borrow money from a private lender for what we lack for the 20% down payment, plus closing costs, which is about $200,000 (property is $1,450,000). 

Issues: 

1. Most private lenders want to be first lien holder.

2. Conventional lenders don't want borrowed money to be used for the down payment. We understand a way around this is to borrow the money at least 60 days before closing so underwriters won't see it as borrowed money that is strictly used for this down-payment. But one thing that we definitely can't do is have a second lien holder bring down-payment funds as a part of the closing because the primary (conventional) lender will not allow that. This means the $200,000 would have to be either a second mortgage on another one of our properties, unsecured, or just creatively collateralized on something else.We'd be willing to let a private lender hold another property, or multiple properties, as collateral, but not sure where to even find someone who'd be interested in doing this.

We'd be willing to pay a high interest rate..we were thinking 10% interest, amortized at 15 years, with a 5 year balloon. 

Does anyone have any advice on where to find such a private lender that would be willing to be creative in what they use as collateral as long as they do have strong collateral? So far, most private lenders I've gotten ahold of are only interested in lending money to purchase fix & flip type deals, or only to be the first lien holder.

We understand cash-out refi/HELOC on other properties is a potential option but there's a pretty solid chance that they wouldn't appraise for what they would need to for us to get that amount out of them, and we don't want to run the risk of that being the primary strategy and then not work out, forcing us to have to follow through with the initial plan of selling a house for a 1031 exchange.

Any help or advice is very appreciated and we look forward to hearing back from y'all!