After a series of excuses and delays, they are saying their bank transfer is coming through Monday and can send me payment then.

When you're about half way towards saving enough for a down payment, reach out to a lender to have them assist you with getting your ducks in a row.  

I went slowly, methodically, and haven't lost one penny.

I have seen a lot of posts on BP Forum regarding transferring a rental property from your personal name to an LLC and have searched the forums in the past trying to gather information. I haven't run across a post with...

I've heard Lland can serve as a down payment for new construction.

This HELOC would cover both down payment and rehab costs, if needed.

With the standard disclaimers about tax advice and how everything depends on your goals: If you have a high income, when you cashout refi you may also able to take the interest payments as a write off, which may make your effective interest rate lower than it would seem. 

I heard about the LLC method a few years ago (forgot it) I don't believe that's a good method for me either.

@Jack Saunders - @Randy Rodenhouse Touched on some really good methods for off market acquistions.

Equity earns 0% interest (inflation will destroy your purchasing power) your real estate investment will Appreciate or Crash regardless of how much down payment you put on your home.