The amount of equity I call pull is less than the cash I have but not significantly less.When doing this analysis it struck me that it may not be worth using a HELOC for the simple fact that the interest rate is ~9%* while the funds in my high yield account are only yielding ~5%*.

If I accept the suggested pricing opportunities it could drop my rates by $100 / night in some cases. 

Even though there is low inventory, interest rates are high, and many properties don't cash flow, look harder there are always deals, you just need to find/make them.

Rent rates have increased so quickly over the last few years.

It's definitely possible to get a loan as a foreigner but the rates will be high(er) and the downpayment required will be as well.

Quote from @Sean Kirk: I'm seeing what seems to be 10%+ cap rates on roofstock.

I’ve had my share of challenging deals too— but the payout made it all worth it.Curious - would you handle the cash-for-keys offer differently next time, or was riding it out the best call?  

Keep looking, but be prepared for higher interest rates with maybe maximum of 65% loan amounts (hopefully more though).

What was the interest rate and when you went to refinance what rate were they offering?

There are plenty out there with fair rates and lower fees.