I think that you’re having night time depression or anxiety, your heart beat is not high but you mentioned that it beats hard. I’ve suffered with both rapid heartbeat and also heavy heartbeat, both were due to anxiety and depression. It’s curious that so many people have this issue and it seems to be affecting them around 3-3:30am., this is also the case with me, the hardest part is trying to get back to sleep. I don’t take sleeping pills but I take 0.5 mg. of Ativan and it helps me to calm down and get back to sleep, I’m not recommending this medication due to all the negative publicity but perhaps you can get help from your doctor to try another medication to help you with this problem. I know that some people are able to handle this by deep breathing or in some cases they get up for a while until it passes, I’m sure that you will find what works best for you with help.