If raising all cash would be my primary method for funding these apartment deals, what would be your guys contingency in order from most preferred to least preferred. 

Utilized a low down payment loan, maxed seller credit, tax proration and closed on the 1st of the month to maximize my cash and acquire this property What was the outcome?

Whatever I do, I would need to do with a HELOC—effectively financing 100% of the property (down payment and closing financed with HELOC, rest of purchase financed with a mortgage). 

Please - do this today: Send her a Notice To Quit for Non-Payment of Rent; you will need to send this to her via USPS with proof of delivery required so you can use it in any legal proceeding.

The lower rate or longer term can also make the payment more affordable. 

Judges will sign off on it, but any judgment obtained by a method of service that is not allowed is void.

@Mitchell RosenbergAnother approach is the elimination method.

I have been trying to save up money but it is not near a down payment for a traditional loan.

I've begun cold calling and looking to alternate methods of finding deals, but if anyone has any advice for overcoming this I'd love to connect.

If you offer more $ for the property than the all cash offers AND you appear to the seller to be highly qualified in the method you are using for sourcing the payment, at some point your offer will be more appealing than the all cash offers.I don't understand why you would consider a 1031 for another property in two years.