I'd get all the paperwork together and file. 

Do yourself a favor, join a LOCAL rental housing owners association.They have the forms you want at a cheap price and usually have attys to review/renew them.As a landlord, accurate paperwork is your best defense.

You have paperwork to support  deduction. 

Most of the time, it's just a matter of paperwork.

I know it will require annual fees and paperwork, but will the accounting of expenses/tax deductions be easier if distibution is contained in LLC filings?

They will request all the paperwork from your tenant and make sure you comply with the law. 

And what paperwork is needed so that the S-Corps can own the LLC?

Then you can mark in as an addendum in the unit's paperwork, that it has working AC and call it good, and then remove the old unit.

One of our investors has a property with someone who was trying to leverage the system, but the tenant didn't fill out the CDC paperwork and provide it to the landlord, and this allowed the eviction to proceed.  

She has provided me with the paperwork that she has been sent regarding payoff and some people in particular at the bank who I may be able to contact and negotiate a lower payoff.