My concerns with leasing would specifically be between property owners who already have tenants in place (And i'm mostly worried about HUD type rentals) which then would require the current lease be terminated, me to come in as new lessee, then to re-lease to the current tenant as a new sublease.

As an Escrow Officer, I can tell you that any money "held" in escrow is not likely to be auto-released without a really well written CAR Addendum and Escrow Amendment.

Now we would like to release some of that equity to buy a rental property - but I don't have the credit score to take two dings, i.e. one for the HELOC and one for the rental mortgage. 

If you gather more jokes you can release 'The Big  Book of Real Estate Investing Jokes' by Ronan.   :-)

There are a number of successful people like Eric Moeller as @Valerie Rogers mentioned who have not only "released" properties, but are creating master lease agreements on a larger scale. 

When and how do you "release" a private mortgage with a payoff from a buyer?

If one tenant would like to assume the entire lease and release the other, they may apply to so do (and be screened appropriately).  

(doing this from memory but I think that is one of the provisions in the standard Texas sales agreement)I thought you had to sign off on the release of the escrow funds

Not sure how they plan to enforce the 90 day rule because I am told airbnb will not release that info to them.

The funds can be put into an escrow account if you wish and needs to be approved by both parties to release funds.