@Jimmy Warr good news with a HML or private lender is that they are very interested in the collateral vs the borrower (borrower is important too) when considering underwriting the opportunity.

Free and Clear Houses - Buy on Private First Mortgages - Create good private terms, like a Moratorium on payments, Subordination, and Substitution of Collateral.6.

Why not keep the rental, use the equity in it to collateralize a loan that along with your  saved cash will get you the next property?  

But they aren't going to accept collateral on just any deal as Jon pointed out. :)

Trusts must be valued annually, admin fees are based on the portfolio under management, discounting saves a bit.Notes held in partnerships establish net worth, if a partner buys out another they will want a discounted market value approach, the buyer will want market value.Notes traded for other assets or used for collateral will be discounted.The market value of assets must be determined for individuals to qualify for medical benefits, this is the lion's share of evaluations.

The 20K is not needed for 30-35 days if they could use homes as collateral.

The rights you have dependon the note having been made from cash or through an equity sale.Foreclosure does not give you the rights of fee simple, you have a collateral interest as secured collateral for the satisfaction of debt.

It will cost you less to use the money you already have and it won't put your personal residence on the line as collateral. 

The MLO will also help you start your collateral file off properly.

Did you mean you used your 5 rental properties as collateral?