You can give legal notice immediately based on your state regulations if they are on M2M otherwise you will be required to give notice XX days prior to the end of their term lease.

Before you do anything else, download and read your local landlord tenant regulations.

Is this some kind of government regulation, or are there other lenders who will still finance a HEL or HELOC? 

Is this possible or is there regulation against it?

However, the challenge with short-term rental is all the HOA regulations prohibiting rentals fewer than 30 days.Heres my question: What is your opinion on the best route to go for house hacking in this market given the constraints?

Remember at the end of the day the banks are told what to do by regulators at the state and federal level they may love you but they may have to take orders from on high. 

You need to figure out how to now fix that mistake.If you have not already done so you need to study/learn all your state landlord tenant regulations....NOW

The correct next step is to download your local landlord/tenant regulations and read them front to back.

There is very little short term rentals as Clark county banned it, Las Vegas heavily regulated it, and everyone assumes North Las Vegas will follow. 

I did property management in CA (years back) and I remember there was no rules or regulations.