So just a few points. I'm just an ER doctor, but you'd be far better off going to your primary care doctor and just asking for a stress test or coronary ct angiogram (not just a "CT with contrast"), than going to the ER and claiming you have chest pain when you don't.
The ER can send you home if everything is normal and you don't have risk factors. And the ER is also the most expensive form of healthcare. Depending on what ER you go to, you'll likely get an EKG, and some blood work. And then if you have any abnormal findings, or sufficient risk factors, given your age, they'll probably keep you overnight and observe you, and maybe get a stress test the next day. Some ERs do coronary CTAs, but not many.
I agree that a stress test might not show if you have blockages, but it will show evidence of clinically significant ischemia. That being said, you could have a large blockage, or a small blockage, and a 100% normal stress test, and still get a heart attack the next day if that blockage, regardless of size, ruptures.
A calcium score will only show you calcified plaques, which are in general low risk for rupture. And a calcium score is designed as a risk stratification tool to determine if you should be on a statin or not.
ERs across the country are already slammed with patients that don't have access to primary care, or whose primary care doctors don't want to see them, or even whose specialists don't want to see them/have time for them. Using the ER as your primary care just clogs the system even further. And something most people don't see behind the scenes are the ER doctors calling the specialists to see patients in the ER, or admit patients. It is frequently a battle - depending on the hospital culture.
If you're going to try to game the system and abuse the ER, please go to a hospital that is used to concierge medicine, and that pays their doctors well, and if you'll have no trouble getting admitted. But still, you might only end up with a stress test, and not a cath or CTA. You really are better off just going to a primary doc and asking for it the CTA, or getting your cardiologist to do it.