Apple support will be able to help you, but if you go in with the attitude that you’ve tried everything and that you know more than they do and don’t listen to them or try what they ask, then you’re just going to get frustrated with them and give up and get nowhere.
It’s quite possible that you do know more than them and it’s quite possible that you’ve already tried everything that they have suggested, but they don’t know that and they need you to try again before they can escalate the issue. They can’t escalate based on your statement “I already tried all that and it didn’t work”
What I would suggest is calling apple back and explaining the problem to them. They’ll have you try everything you’ve already done, but that’s OK. Lose the attitude and walk through the settings with them over the phone. That way they will know that everything is configured correctly. Then leave it plugged in, locked, and connected to WiFi overnight. The next day, when it didn’t work call back and let them know that it’s still not working. They may have a few other things for you to try (that you may or may not have tried before). Humor them and try those things as well and let it go another night, then call back and tell them that it didn’t work again.
Eventually when the front line of support runs out of options they will have no choice but to escalate this case to the engineers who can actually look at the logs and see what’s happening and why it’s failing. It will probably take several days to get to that point (because you’ll need to wait overnight to see if it starts backing up after each iteration of changes) but as long as you keep working with apple you will get there. If you just shut them down and keep the attitude that you’ve already tried everything and they are useless then you’re just shooting yourself in the foot here.
I get that it’s frustrating when you do know what you’re talking about and have to go back to the basics with support, but along the same lines, more often that not issues like this are caused when someone who does know what they’re doing misses a step or overlooks a setting, so it’s important for the support person to go back to step one and go over all the settings that you’ve already checked 30 times. There are certainly cases where everything is configured correctly and it’s still not working, but they need to start at the beginning and be absolutely certain that is what’s happening before it gets escalated.