First of all when you say coil are you talking about your condenser (outsied the house) or your evaporator (inside the house). If it's your condenser, even contractors grade generally has at least a 5 yr. warranty.
Second, as far as leak testing, there are all kinds of leak detectors that should detect your freon problem on the spot. If they say they can't you might want to look for another company. As far as your coil freezing up, thast could also be caused by low airflow over the coil. Check your blower motor and your filters to make sure they are not plugged.

We has almost the same problem happen to us this week,
we have a 7 year old lennox and the inside "A-COIL" is so badly rusted and clogged up that we are going to REPLACE IT at $500.oo.and get a parts guarantee.

Our other choice was a $350 clean with no Guarantee Since we have a central unit (lennox) we are going to replace the old 3 ton coil to a (3 1/2 ton goodman) one. we are having all the duct work blowen out to clear it from as much pet hair as we can, ( too many animals in our house) and adding 2 larger air intakes to accomadate the upgrade. just that part of our entire heating and air upgrade is going to cost us parts and labor less then a new system which is not outdated and in good shape. hope this helps

Depending on how severe the leak is, you should consider a new product which is now available. It is like "stop leak" for air conditioners. Some freon leaks are in the lineset inside the wall (very difficult and expensive to find).

Your coil could be freezing up because you need to change the furnace filter. And don't put in the expensive ones that are supposed to filter out a bunch of stuff. This restricts the air flow, causing the coil to freeze up. Get a normal filter and see what happens.

The unit is just at 6 years old.

The guy said that he could do the test for the leak (for $250) but in his "20 years of experience" every unit he's worked on like this that has a leak always has one in the inside evaporator coil.

I don't know what kind of service tech you have but I would look for somebody who doesn't wear a mask. The first time he charged you for the freon anybody worth his salt would have taken a leak test. To take a test now he must again put freon in and then actually use his equiptment. For 250.00 labor he could put a new coil in. I'm assuming you have a furnace with an A-COIL in the top with access to it. To replace the coil he has to gain access to it by removing the panel, then remove the lines and remove the coil and install a new one, repace the freon and the test his work for leaks anyway. Unless it's an unusual job it should take about 2hrs. with a nap. As far as 1500.00 ask the guy if your paying for his addition on his house. Seriously, I would look for another opinion before dealing with this guy. Even if you end up getting another evaporator you don't have to change your condenser.(outside unit). The 500.00 review price is just about what you should be looking for. Good Luck.