Handicap and half damage ratio is definitely very good for practicing anything that requires a lot of inputs after hitting someone, so shuffling, shuffling on shield, shuffled aerials into shine grab, multishines, etc.
Make sure to practice each of the aerials, it's important to be able to hit the l cancel after drill regardless of when you start hitting them and from a full jump, jump/drop from a platform, jump from the ledge, etc. Making that l cancel can be the difference between starting a combo or getting comboed yourself.
Definitely practice with Ice Climbers, a lot of Ice Climber players like to try to force you to miss your l cancel by angling their shield, and lightshielding with one IC and regular shielding with the other.
Doing aerials without hitting anything is also important to learn, and thankfully the only time the drill l cancel timing is the same as the nair, bair, fair, and uair is if you're hitting nothing. The drill also has the most lag so if you're having a hard time spotting the l cancels at first just work on doing the drill l cancel without hitting anything to get the empty timing down, then apply it to the other aerials to see what they look like. Spotting when you miss the l cancel is probably one of the most important things to getting better at the timing, because once you spot it it becomes more obvious what the timing should be, and you learn how to adjust the timing without having to slow it down.
I personally think changing the speed in training mode is horrible, if you need to learn how to do the inputs with your hands just do it on your controller without playing a game. This is just personal preference though, a lot of musicians get a lot out of slowing things down then bringing it up to tempo, so whatever floats your boat.