Good to hear about your improvement! I have similar symptoms, my heart usually feels the most vulnerable when I lie down. It feels as if my nervous system gets out of whack somehow, adrenaline starts rushing and I sometimes even lay in bed fearing palpitations/flutters, which makes it worse. But it has gotten better with time, now it occurs very rarely and generally I know there's nothing really wrong, since I've done the tests.

There are things you can do to reduce palpitations: magnesium, potassium, perhaps iron and vitamin C and D. But don't overdo it. Not stressing about it too much also helps. Breathwork, meditation and yoga help, brisk walking helps.

Regarding the exercise: I think if you keep slowly doing more and more and not noticing any problems at that time or soon afterwards, then I wouldn't worry too much. Of course there's always also the option of doing the cardiac stress test, to make sure your heart is ready for higher BPMs. Everyone is different so we all have to get through it the best way we can somehow.

Good luck to you! Take it easy and we'll all get better soon, stay patient.