We were renting out our house, living in the in-laws’ basement, experiencing medical and other hardships, and had $65K of debt (medical, consumer, vehicle, college, etc.).

Those just aren't great set ups, particularly for traveling medical professionals how work long hours and need quiet when they're not working. 

If it were me, I would want to know what the debt is for; medical, student loans, alimony/child support payments, shopping sprees.

Meaning after opening the HELOC for 10 years it will cease to be a HELOC.

I contribute 6% to my 401k (with a 4% company match) and all medical/benefits are fully covered by my employer. 

Demand has historically been high for travel with the theme parks, weekly military basic training graduations, medical district, and historic downtown draw (Alamo, Riverwalk, etc).

Furthermore, your E-4 really has a lot more take home pay because they don't have to pay for medical benefits, retirement, life insurance, etc. and much of their compensation (think Basic Allowance for Housing or BA for Sustenance) isn't classified as "pay" and therefore it's not taxed.

@Angelo Mart That is actually really interesting you would say that because I've been finding that area more and more attractive in terms of buying rental properties for students given its close proximity to the law school / medical school / NJIT.  

Even though furnished finder was first created (and still labels itself as 'travel nurse housing demand') to cater to travel nurses, they recently published an article about searches for furnished rentals by non-medical travelers exceeded medical travelers for the first time and they expect that trend to continue.

You could have gone with a cease and desist but they may have just used another STR method/website or an MTR.