If you have a good relationship with someone, you can get a 9% loan, if not it can range from 10% to 18% and points can be in play. 

SFH homes under $250k are in very high demand right now so I think it would depend on the rental income numbers. 

Incredibly strong housing demand, a crippling 1.5 months of inventory, and ongoing affordability concerns produced year over year declines last month in new listings, active listings, and pending sales in the City of Austin.

This is from the statute "197.432 Sale of tax certificates for unpaid taxes" See section (14):(13) The holder of a tax certificate may not directly, through an agent, or otherwise initiate contact with the owner of property upon which he or she holds a tax certificate to encourage or demand payment until 2 years after April 1 of the year of issuance of the tax certificate.(14) Any holder of a tax certificate who, prior to the date 2 years after April 1 of the year of issuance of the tax certificate, initiates, or whose agent initiates, contact with the property owner upon which he or she holds a certificate encouraging or demanding payment may be barred by the tax collector from bidding at a tax certificate sale.

Make an offer, get it into escrow, get a payoff demand, close, enjoy your new property.

At some point you've just got to play the hand your dealt.

There's a how to do it element that comes into play to significantly reduce the risk of an out of state investor having a bad experience. 

I understand that there are a few variables at play, but in general, How much equity must you have in your primary residence to qualify for a HELOC?

There is a factor called Cap Rate that is market dependent and it plays an important role as it can change the value greatly.

Playing with this gives you a quick and easy way to look at one metric (cash flow) and get your pricing boundaries.