If the total for the month is $30 (which would be determined a month later) then the tenant might owe him $10 and me $20.After closing, the owner has no recourse against the tenant to pay him the $10 he is owed (because he is transferring me the deposit) so he wants it paid at closing.  

(i.e. higher than just a security deposit would be)

Because after every Refinance, you have your deposit back for your NEXT Buy!

Owes about $1700 between missing rent and damage/repairs (I've already deducted his security deposit). 

You need to explain what an "option fee" is in your question.If someone purchased an option from you, then the money is yours.If someone has deposited a fee to secure an option, such as a right to purchase dependent on a satisfaction of inspection or engineering report, then the money is not yours.If the money is not yours you might want it held in a title company's escrow account (or an attorney's) with a written escrow agreement describing what the deal is.If you hold the money, and it is not yours, state and federal law might consider you a "fiduciary."

If we have to demand the deposit, as the law says we should do, it says to do it by certified mail.

Offer the security deposit for possession in return.

I have no idea what kind of repairs/work will be needed until it is vacant.But yes, you need to check local laws, but you likely can keep the deposit to cover the repairs and such.

On the back of the check they just indicate "For Deposit Only XXXXXXX". 

I take one application at a time, unless they have not put up their holding deposit.