I have made, literally (strict definition), hundreds of calls to Apple Phone tech support.
I bought my very first computer (having never used a computer before) about 21/2 years ago. When I first got it, I was on the phone with Apple 10 times a day. More recently, knowing a bit more about my machine, the frequency of my calls has declined precipitously.
Me experience is that the first line techs, if they do not resolve your problem fairly quickly, will always respond positively if you (politely) request that you be bumped up to a Senior Tech.
The Senior techs have access to a screen sharing mode (with no control over your computer...they see your screen and can move a mouse pointer on your screen to help direct you). In the hundreds of calls, the Senior techs have not been able to resolve my problem 3 or 4 times. At that point, I take my device to my local Apple Store. I am fortunate to have one 20 minutes away. The problems have always been solved there.
So, my experience is...spend some time with the first line tech. If after about 30 minutes or so the problem is not resolved, (politely) request being bumped up to a Senior Tech. They will really bust their ass to resolve your problem.
On the rare occasion they can't fix the issue...then I can just hope that you have an Apple Store or authorized repair shop within striking distance.
