Definitely do a leak down test. you can pick up an el cheapo leak down tester at harbor freight for about 40ish. Also check your oil to see if there is any coolant in it. Once you establish those 2 things you will have a much better idea if its actually the HG.
300 for labor is ridiculous. To do a HG you have to pull the motor, remove all the accessories on the front, pull the timing cover, pull the belt off while immobilizing the timing gears so you don't bend the valves, remove the cams and buckets, (keeping them all separate and labeled) just to get access to the bolts you need to remove to pull the head. And that's just the big things I can think of, there's a bunch of misc steps in between those that need to be done.
So for 300 labor: you friend is either a master subie mechanic and is hooking you up, or he has no idea what hes about to get himself into.
Just my .02