You are taking two very potent inhibitors of noradrenaline reuptake (Ami + Cymbalta) which will make the amount of noradrenaline in your body increase. 15 mg of Propranolol is close to nothing. For beta blockers to have a true effect on heart rate, you would need much higher dose. 15 mg can help a bit on palpitations, but it will probably not reduce the heart rate so much.
In my case, my heart rate during stress and anxiety drops about 10 bpm per 100 mg of Metoprolol I take daily. At 200 mg, my heart rate at work after three cups of coffee and an intense meeting is about 65 rather than 85 as it would be without.
Maybe you should get a cardiac ultrasound just to objectively measure the pumping force of your heart? If your blood pressure gets low (common side effect of Ami) that too will increase the heart rate.
It's not the beta blockers, its the amtriptyline and Cymbalta combo (i'm willing to bet on it). Tachycardia is a well known side effect of that particular class of (old) antidepressants. Cymbalta is a SRNI, so you're getting a double whammy on the tachycardia side effect as the previous respondent pointed out. You may want to check with your Dr to switch out your AD meds.
I wanted to add; Amitriptyline also have anticholinergic effects. A bit like atropine. It blocks the "brake pedal" in the nerve system and can cause tachycardia.
Maybe you could ask your doctor for newer AD's without this side effect?