I am one that hates to give up the money to have things fixed but then I also hate to waste time, effort and money on things that are too far above my training. Air conditioning is one of those things which I find has a lot of things which may seem very simple once we get down to the specific p[arts, but there are way too many of those parts to fail.
When I hear air is not cooling like it should, I know just enough to be dangerous at times!
I have a feeling you are correct in letting better trained people look at this one. Just due to the really large number of things that might make it not put out the cool air!
First we have to figure out if the problem is air equipment is not cooling it right or if it is cooling but the vents and mix controls are not letting that cool get to us!
Getting the cooling done is one thing but we also have to get the heat shut off to really get anything done!
And that alone can get into all the small points that we can spend a lot of time trying to chase down something as simple as a leak in a small part of the vacuum system that moves the controls!
A leak in a vacuum line can mean the flaps that control which way the air moves stop working. Or it may just be a funky flap movement that sticks? Then we need to stop the hot water going through the heater or we are trying to heat and cool at the same time and heat often wins that contest.
Just a lot of weird little things that most of us may not even know are in there, let alone how to fix them.
Bottom line is that I think you are making the right choice!
But I still hate to pay for that service!