The initial deposit doesn't need to be private. 

And what I am personally seeing the Market place today.Commercial bank/ community bank were you have significant deposit relationship and long term relation ship..   7 to 10% plus 1/2 to 1.5 points.. these are relationship and experience and capacity lenders..

These are not refundable, so you give this diligence fee AND an earnest money deposit which is refundable.For that, before you make any offers be really sure what you're buying.

I have always been a stellar tenant, always recieve my deposit back never ever have left any place I've resided at without making it look like it did or as close to when I received it.

My question is can I legally keep their security deposit?

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.