What to recommend will depend on your control scheme preferences. For example, I play with tilt set to my right stick (The ATTACK option) which helps me mitigate mistaking tilts during heated battles. (Which is also good when you want more control over your aerials, but that's a different question) If Tap Jump is off, I've practiced using the 11 o'clock and 1 o'clock positions on the left stick for quick turnarounds instead of trying to just slightly pressure the stick in a direction. (Just like the right stick reasoning, in the heat of battle I maybe too forced on my stick and you can't dash when hitting those angles since only the sticks position on the x axis counts)
I've found practicing on the 3DS does help a little, since there is no right stick on there for most users (and those with the New models can only smash with the c-nub) and you're forced to work with the Circle Pad. The Circle Pad is also a flat input compared to the raised nobs on the Pro controllers and equivalent, so it takes less pressure to do the same job. (You won't be fighting against a Sphere Circumference for resistance!) The equivalent pressure required for the 3DS on the Pro controller's sticks (or GCN, or Gamepad, etc) will move the stick less so your muscle memory will work towards your advantage here.
These are some of the things that have helped me. I'm still not perfect, but these have upped my game so much since I started.