Whatever you do, be sure you do engage an air-con contractor do to quarterly maintenance. It will be your cost but you should forward "copies" of the quarterly services to the landlord anyway.
A mate of mine just bought a
condo here in the same condo that he was renting in (different unit) when his lease was finished they virtually refinished the flat at his expense (kept his entire deposit) because the said the the aircon's caused all the water damage in the flat (along with "black" hairs clogging the drains). When the agent was showing the
property he did note the peeling paint but did not say anything to him at all about seeing about rectifying the problem. I saw their response this morning (mate emailed me a copy of the letter) blaming him for not getting quarterly aircon maintenance contract, therefore apportioning the wall damage, parquet floor darkening from aircon overflow drains and condensate (even the the floor darkening was there when he moved in (I know, I helped him move in). SFA he can do about it as they are saying the repairs were more than the deposit but they are being kind as to not require additional funds to cover costs of repairs. It's total BS but this is Singapore where the tenant has no recourse at all.
If you don't get an aircon maintenance contract along with the paperwork indicating when they do the maintenance, the landlord will find a way to stuff you up. So, I think you guys know what to do regarding the last months rent before your lease expires.