We have them check the heating coils as well as cooling and refrigerant.

Pairing that with a lighter handyman visit to flush the drain, check the coils, and look over exterior items seems like a good balance between cost and prevention.Since your property manager is already doing inspections twice a year, this really just adds another layer of protection rather than duplicating effort.

Few months ago they came to do the maintenance and said the coil is dirty and need to put in 1.3K to clean it.  

No icemakers or water dispensers in fridges; no sensors or other doodads in washers & dryers; coil stoves or basic smooth tops; basic dishwashers (I prefer the dial timer models but they're getting real hard to find).

The static pressure across the coils is probably killing the unit, if you dampen the registers it will only raise the static pressure.

The unit worked but the coils were damaged by dogs.

My personal preference is old style coil tops, because the renters tend to ruin smooth tops with their cheap pots, but I'd do a cheap smooth top before gas. 

After going into the attic they noticed the real problem was coming from the coil in the AC unit but had already spread...

All of the metal for the metal roof, is imported as coils for the roof and flat metal for the beams/rafters and purloins. 

I have a HVAC installer coming to give me an estimate for a complete install, Condenser, Furnace, A-coil, ducting, fuse box.