No, lenders will want their position secured and with no equity there is no place to be secured. 

Has anyone had any experience with lenders that will still do HELOCS for short times on deed or does that matter?

Then what would the contract/term look like with the private lender for the 20% down?

They seemed like nice people but I ended up rejecting them.

That aside, if I were, then I'd likely either go out of state as a lender which is more passive or as a partner in a private placement (syndications, etc.) whereby if the general partner makes more money it means that I'm making more money too ...

You would have to pretty much get a property for free in order to qualify.I have submitted two properties to their underwriters, and both were rejected because of last minute requirements that changed the lending criteria.I paid $2,000 (one year's worth) in order to be able to receive funding.

I am buying a flip house and use a portfolio lender to finance it.

Due to lackluster service and better pricing elsewhere, I did so with a different lender.Since then, I've learned about the concept early payoff recapture, and, not wanting to cause any problems for my previous lender, I inquired about the recapture period on the previous loan.  

What is the best approach when seeking private money lenders? 

I know the lender is Citibank the deed is subject to their foreclosure but according to the tax records it's been in this stage for 6 years already.I want to purchase the place so I can eventually rent it out.