It appears your confusion on the 2nd place is because you're factoring in mortgage debt.

We have about $20,000 in student debt from both my wife and I, have $1,500 in savings and have a baby girl due to join our family at the beginning of July (she will be our first and we are so excited!).

With the help of the family member, we got all 15 heirs to sign with us and said due tot he complexity of the deal, we were able to payoff the remaining debts and put some money in each of their pockets.

On the other hand, having rental income without having to worry about another debt is nice, but then the equity is locked up in the house and no tax benefit. 

I'm trying to work out the numbers but it seems like without a substantial down payment, cash flow is impossible thus eliminating any type of rental/brrrr strategy.

HELOCs are better for short term debt such as flips, cash out refinances are better for long term debt such as down payments on buy and hold.You will have to do some "dialing for dollars" to find a regional bank or credit union that'll do a HELOC on a rental. 

It may be sensible to retire this debt prior to paying off our HELOC. 

This place also purchased the debt of TransAmerica Financial Solutions.

This definitely wouldn’t help...but they had accumulated quite some debt from the revitalization project, it seems 

If so, the lender will pay off the existing debt and take 1st DOT for sure.