Sorry you're not feeling well. I can relate, and it's not fun waking up with wacky feelings in your chest!
I'm 52, still in perimenopause (though getting close to official menopause) and have been having similar symptoms to what you are describing, off and on for a couple years.
(At times my hormones fluctuate considerably from day to day.) My early morning (2-5 a.m.) palpitations are sporadic, appear to be worsened by stress, and are more likely to appear when I've fallen off my regular exercise schedule. (Exercise seems to help normalize my hormones, as does a low concentrated sweets diet.) Also, sometimes I wake up and feel irregularities after having a nightmare or an intense dream. Does this ever happen to you? From what I understand, the adrenaline rush brings on palpitations.
Perimenopause and fluctuating hormones may be contributing to your symptoms. There is a good explanation of the impact of hormones at
http://my.clevelandclinic.org/heart/women/conditions_arrythmia.aspx (Scroll way down to "Hormones and Irregular Heart Beats")
Have you been under a lot of stress the past week or two?
Stress can bring palpitations on, but as you know, it's not a good idea, especially for women because their hearts and bodies often behave differently than men's, to automatically chalk up symptoms to stress without seeing a doctor for confirmation.
Have you worn a 48-hour Holter monitor? If not, I would see your cardiologist and ask for a Holter, so you can find out what's really happening early morning when you have symptoms--what your heart rate is and what your heart rhythm is. Keep in mind that if the cardiologist wants to do a stress test, false positives are more common in women during perimenopause. (I experienced this as well) I think personally, I'd ask for the Holter monitor FIRST before the stress test, if your doctor is willing to do it.
Also, have they checked your thyroid levels within the last couple weeks to make sure you're not hyperthyroid? That can cause arrthymias including atrial fibrillation.
Please keep us informed as to how things come out. Take care!