There can be several reasons for losing compression in a cylinder.
Either there is no air coming in, of there is a (big) leak.
The first thing to do is to test with compressed air if and where it leaks, this is a very simple test. If the air goes to the bottom (carter) you have a hole in the piston (bad), If it goes to the exhaust (with the valves closed) the exhaust valve is burnt (less bad), if it comes out at the side or front the gasket is blown (even less bad).
Of course there are other possibilities, but they make a lot of noise.
For looking inside a cylinder you don’t have to pull the head, with a scope it is very easy to loo through a sparkplug hole.

The only reason this dealer can have to pull the head is to make sure you must stay with them and you are forced to pay whatever they charge you. Without a head you can’t drive and since you owe them $600 they can work the bill up from there.

So take your car out and find a independent shop. In general the price/quality can be measured by the amount of grease on the owners hands. Information about independent shops can be obtained by family, neighbours, people at gas stations, taxi’s, or anyone on the street driving an old car. If you make some work of it you can get a good picture of local car shops in a reasonable short time. A good independent shop gets it customers through other customers and not because of a Mercedes sign.