The problem is that the process takes extra steps and tax claim bureaus typically don't --- or won't care to --- take the correct steps to discharge it.

But just a random stab in the dark they want you to overpay IMO 500 extra for the headache of a STR isn’t worth it, plus you’d have to furnish it and pay for all the utilities.  

Anything else over that is extra.

Just at a glance without running numbers I'd think the extra cashflow, and not losing those points for each refi, the HELOC even at a higher APR would win. 

Edward, can you give more details about the project?

I have two options in front of me either to obtain a rehab loan, which will cost me $10k for six months ( points, fees, interest) or just finance the entire deal with my own money (cash).The rehab loan will enable me to obtain an additional property, so in six months i'll have two properties ( one with the loan, another with my cash)  but it'll cost me an extra $10k (on top of the regular down-payment which in any case i'll have to lay out) .

Depending on the duration of your tenant, you can calculate the amount of extra money needed to set aside for this expense.

From about February 2018 we decided things were getting serious and I spent enough time at her house that I might as well put my home on Airbnb to make a little extra income since we spend enough time at each others homes (currently we have made about $10k off of my home on Airbnb). 

I truly appreciate you going into such detail.

Either way there is a refinance so you would be looking at doing an extra loan.