YOLOGeneral principle of taxation: to take a deduction, you mustA. be legally response for this payment and B. actually make the paymentThe conclusion should be obvious.

I have a large lump sum saved in an investment account for down-payment and any additional costs.

My concern is doing the cash out refi on my other rental and causing a new and much higher payment on it that I can't just pay off like a loan.

For example, you might leave $10,000–$25,000 in the deal, end up with a $3,000 monthly payment, and only collect $3,000 (or slightly less) in rent.This applies to my local market and primarily to Class B or higher real estate.You’re better off finding a solid property that needs only light cosmetic work (e.g., paint, flooring, or perhaps a kitchen or bathroom remodel), buying it at a decent discount, and putting down at least 25%.

Can I get a loan for the down payment / construction costs2.

In this case, your monthly payment with 20% down will have a good MARKET rate if your DTI works with a much lower month payment and no mortgage insurance(MI).

Despite the program's claims of providing exceptional training and support, my experience with Kristin has been far from satisfactory.First and foremost, I find it necessary to address the issue of non-payment.

I even bought 3 properties in one day using the HELOC to fund the down payment on each of those purchases. 

Perhaps we "buy" the house from them for the $328K balance to satisfy the lender and don't need a large down payment and then have a separate contract with them to pay $x per month until we've paid the full $172K amount.

How long have you owned these, and how much is rent vs the payment?