They would also automatically update all batch deposits in the bank transactions so you wouldn't have to match them manually.

Looking at it as depositing into a long term savings account.

That's a private agreement between you and your LLC and that loan is not recorded in any banking data base that it would be put on any credit report.You are fine just depositing the money and then moving forward.

Start depositing all of the rent into that account while paying expenses for that property out of that account.

Same with putting a larger deposit down to make your monthly payments lower doesn't mean you are cash flowing more as you put more money down to 'force' the cash flow.What matters most is that you are happy with the numbers and they work for you.

On Dec 12th, I was awarded back rent by JP court but tenant filed appeal (month deposit is waived as bond if you claim not to have any $$$). 

You need to have "Skin" in the game meaning your money or "Family" money.You can receive "gift funds" from a "Family" member if money was given to a family member and then given to you as a gift from family it would work.Keep in mind even if the seller gives you money the bank/lender will see the deposit into your account since they ask for (2) months of bank statements.

How are you collecting a deposit, or putting holds on credit cards, for your STR direct bookings?

Also you need to figure out how you intend to cover inevitable property damage done by guests but there are plenty of solutions for that in the marketplace where guests pay a flat fee per reservation in lieu of a deposit and you get covered for an assortment of potential issues (bad checks, credit card chargebacks, fraud, personal property damage, etc.)  

Shouldn't your broker be involved in this security deposit issue?