If you let go of the ledge going down with the control stick you fast fall, so the timing is harder. If you're doing it that way that's probably why you have trouble getting high enough. Here are my inputs for both ledgedash and RLD assuming I'm on the left ledge:
Ledgedash:
,
+
,
+
RLD:
,
+
,
+
I flick the control stick back and forth like a pivot to get it out in time. As you said, I have similar inputs for both so it's easy to switch between the two seemlessly. And this motion was easy to get into my muscle memory because it's a very distinct flick. I think you'd have a lot more success with this method than using the c stick to let go of the ledge because then you have to bring your thumb all the way up to Y or X after, making it harder to be as precise.
Oh and I totally know what you mean by the fp aerials being harder on the right side. I can't do fp bair on the right side with the c stick, so I just do a and control stick for that, but I only do that if I really want to get out a fp bair. For example, doing fh bair into landing bair or wl.