You should get used to using the C-stick for aerials, it gives you much better control over your aerials. I imagine it would be really hard to space retreating bairs with the analog stick. I use Y to jump and C-stick for all aerials (except for nair and to do thunderboot), and I'm perfectly comfortable with it. You might be hitting the C-stick too hard, or so too long so that why it feels too slow? I just press Y and kinda flick the C-stick upwards to SH upair. If I'm going for an up-air juggle, I just spam flick the C-stick up to buffer the next up-air so I don't have to time it. I usually flick it 3 times to do a 2 up-air juggle.
It might maybe be the way you're holding the controller? My thumb never rests on the controller at all, it kind of just hovers on slightly above A and B. I just quickly tap the Y button and instantly put my thumb on the B button, and by doing that I can pretty much do anything in the SH since the C-stick is so close. I pretty much do all that out of muscle memory, I only actually looked at my hands while playing about 5 minutes ago to see how it's like
If up-air -> uptilt is hard for you, then you can use C-stick for up-tilt too. Just hold up on the analog stick, and flick up on the C-stick and you should uptilt. I personally don't, but if that's what you want then
I use my controller the default way, cept for tap jump, I turned that off.
I'd say you should just get used to C-stick for aerials, you might not see it or feel it right away, but you get MUCH better control when you do. For an immediate example, go up-air juggle ganon at low %, sometimes he falls too fast for your next up-air. If you use C-stick, you can easily fast fall to connect your next hit.
I think when I needed to get used to using C-stick for aerials, I used Marth and just practiced spacing with fairs until I was pretty comfortable with it, and then it just automatically transferred over with all my other aerials. Think you should try what I did.