In a lease option or subject to agreement, it is my understanding that I as the investor would pay the seller monthly payments.  

It isn't easy to find extra money for a down payment, at this point and so it kind of leaves us in an undesireable spot to be in.

I pay an introductory rate for the first two years, my current payment on 21k is 71.34 a month.

I want to refinance this property and take out the money to buy another rental property (or at least put a good down payment for one or two).

Typical bank draw cycles are at least 30 days plus a few days for the bank to process.If your contract stated payment immediately upon completion then you have a solid argument.

As I do not make much to put a whole lot for down payments.

Myself and my Wife currently own a home (in my wife's name) that I make the payment on.

RoI I listed is after my payment and interest.

Some people look at cash flow as the renter giving you back your own money (down payment) a little at a time.

As an example, let's say the person is about to go to foreclosure because they got behind in their payments due to a job loss for 4 months, but have now found employment, but can't get the back payments caught up.