Word. I've run into a lot of people over the years that didn't realize this type of thing existed, and if they had something with a fan blowing air through ductwork it automatically meant they had a standard HVAC system.

The only things I can suggest you do is to make sure your air filter is good, and if you can look at the indoor coil of your AC system to make sure it isn't clogged with crap (it being an apartment, it wouldn't' surprise me if it was) as well as the coils on the outdoor unit. If the filter is replaced regularly, the indoor coil should be fine, but if it isn't, pictures of the dirty coil will give maintenance an idea of what they need to do, and give you more evidence that something needs to be done. One thing I have noticed is the coils on the condenser unit outside tends to be neglected by everyone, from homeowners to businessowners, but they should be cleaned periodically (once a year) as pollen, dust, tree and other plant debris, etc. can coat and clog up the fins, making the units rather inefficient. I hit mine up every year after the tree pollen is done with simple green, let it soak for 15 minutes, and then hit it with a hose from the inside out, but if you have access to the outdoor unit and "accidently" spray it with simple green and let the rain wash it off, it might help some if it's really dirty. Just don't tell maintenance that you've done anything like that as they'll blame you for something, since management companies just seem to be like that...

I wish you luck in this fight for proper climate control...