Patmob is right, as always. As a healthy 24 year old whose preliminary heart tests found nothing abnormal, there's no way your doctor or your insurance company is going to approve those tests. I know they didn't for me when I was 30.
Besides, you need to realize that medical testing does not lead to peace of mind. I tried that, too. Right now, you THINK certainty is just on the other side of that test result, but I promise you, there is always a doctor to doubt or a result to question—always.
You acknowledge the fact that anxiety is largely subconscious, and part of the reason why it's so much worse in the morning is because your stress hormones are NATURALLY higher as you wake up. The extra coristol and adrenaline are there to help make sure your body gets going. Since your stress levels are higher because of the subconscious anxiety, your body is therefore more reactive, and hence your higher heart rate.
Have your talked to your doctor about possible anxiety treatment? If he has a psych background, he should have some significant insight into this matter. Do you have a church home? Ask people there to pray for you—I did that, too, and it helped a lot when I thought I just couldn't handle it anymore. I think we all, as anxious types, want to alleviate all our symptoms right away, and it's hard to sit in the discomfort and fear that health anxiety brings. But, unfortunately, it just doesn't work that way. Getting past anxiety requires a lot of effort and a lot of patience. Your stress levels didn't reach reactive states overnight, so getting them back to a non-reactive state isn't going to happen overnight. Find an anxiety treatment regime that works for you, and stick to it. You won't see results right away, but you will over time.