If you are not living in it, and have a decent down payment, it is very posable you might be able to arrange private financing at 8-9% with a ballon set at a point when you can reasonably expect to obtain financing.Another considerations would be to look for a tax sale property.  

Loan aside you would be smart to have some form of legal arrangement in place to deal with the property going forward.

What sort of arrangement would you work out in this instance?

I’ve run into an unexpected issue with keeping up with all of the landlords that are willing to do this arrangement!

That arrangement seemed odd to me and I'm suprised others here do the same.

It can probably be arranged at escrow to pay off the HELOC directly with the funds coming from the refinance.This depends on whether you ran your numbers correctly and you have enough to pay off the HELOC from the refinance. 

(e) “Service” means and includes, but is not limited to, any of the following:(1) Debt, budget, or financial counseling of any type.(2) Receiving money for the purpose of distributing it to creditors in payment or partial payment of any obligation secured by a lien on a residence in foreclosure.(3) Contacting creditors on behalf of an owner of a residence in foreclosure.(4) Arranging or attempting to arrange for an extension of the period within which the owner of a residence in foreclosure may cure his or her default and reinstate his or her obligation pursuant to Section 2924c.(5) Arranging or attempting to arrange for any delay or postponement of the time of sale of the residence in foreclosure.(6) Advising the filing of any document or assisting in any manner in the preparation of any document for filing with any bankruptcy court.(7) Giving any advice, explanation, or instruction to an owner of a residence in foreclosure which in any manner relates to the cure of a default in or the reinstatement of an obligation secured by a lien on the residence in foreclosure, the full satisfaction of that obligation, or the postponement or avoidance of a sale of a residence in foreclosure pursuant to a power of sale contained in any deed of trust.(8) Arranging or attempting to arrange for the payment by the beneficiary, mortgagee, trustee under a power of sale, or counsel for the beneficiary, mortgagee, or trustee, of the remaining proceeds to which the owner is entitled from a foreclosure sale of the owner’s residence in foreclosure.

As of mid-summer, they were saying that 13 of the planned 80 houses were spoken for, with deposits down and financing arranged.

Also, you could set your checkout times to 10 AM - 4PM, keep the length of time their allowed to book short (1-3 days), and arrange showings between the checkout times. 

Another method is to simply bring the deal to another investor and work out some type of arrangement between you two.