I then follow up with the lead to usually find a buyer on the other line very confused because they already have an agent and thought I was the listing agent.

Rehab and get the house rented.You can even start the refi a little before you finish the rehab if you want - assuming you have a renter lined up and ready to go.I once had a refi done on a house I bought within 45 days or so of the purchase.

See how nice and helpful people can be when the situation is correctly stated :) @John Andruszka   SO Ya your next step is post pay or quit then file for non-payment, eviction, she's not gonna pay you a dime. is my bet and I bet I'd win that bet..You have no guarantee she'll pay rent, you've given her 2+ extra weeks to move..

No matter what the situation is you have to make it to the finish line... 

I have 250K on a line of credit with interest at an Annual Percentage rate of 5% that I can utilize.

I hand it to all you guys that are able to invest across 6 state lines. 

Take out a 100% Home Equity Loan (not line of credit) from my credit union on my personal home and put some cash with the equity loan for a cash purchase.

Other contractors I've spoken with are lined up 3 months out.

I’ve always heard the refinance discussed as a mortgage - but I’m wondering why not a Home Equity line of credit instead?

All of them have  Residential loan products for investment properties.  15, 20, and 30 year mortgages.You can also try on-line Lenders like LendingTree or Quicken Loans.