Yes, it does sound like dysfunction of the autonomic nervous system. Your rhythm is sinus in nature if I understand you correctly.
An electrophysiologist SHOULD be familiar with the cardiac part of dysautonomia.
Ask the doctor about a norepinephrine test while standing and if they haven't run it already, a complete iron panel, even if your CBC (complete blood count) came back as normal. (I've been iron deficient when my CBC was normal and felt it made my symptoms worsen- such as shortness of breath and worse tachycardia and I had fatigue.)
To check regarding hypovolemia, you might ask for renin and aldosterone levels labs taken while standing (normally low in hypovolemic patients). And another test in regards to volume is a 24 hour urine test for sodium level.
You may have to find a sympathetic doctor willing to order some of these tests (they hopefully will be willing to at least do an iron panel) or go to a center/doctor specializing in dysautonomia:
You are, it sounds like, experiencing bradycardia (slower than normal) heart rate when you sleep and your heart is racing when you stand to prevent you from passing out. The fact your blood pressure stays about the same or goes up a little shows your body is doing a good job compensating to keep you from passing out.
I agree with Maritza about P.O.T.S. (postural orthostatic tachycardia syndrome)- I think it is very likely. With P.O.T.S., the heart rate goes up 30+ beats per minute with standing.
An electrophysiologist would likely want to run a tilt table test, but if you can prove it so dramatically, as you are describing, without going through that test and the cardiologist is familiar with P.O.T.S. and will do orthostatic blood pressures on you there in the office (lie down on the exam table for about ten minutes before they take the numbers, stand for at least one minute before they again take your blood pressure and pulse, etc.), you might consider avoiding the tilt table test, as it's not a pleasant one for a lot of people.
The other criteria for a P.O.T.S. diagnosis
(besides the heart rate going up with standing 30+ beats per minute in absence of an underlying explanation like severe anemia, dehydration, or a panic attack when a person stands up; and I think they may look at length of time this has been happening also)
is a standing norepinephrine level- I believe it has to be over 600 ng/mL. (I never was tested for when diagnosed via tilt table test.)