I believe dry hands are a blessing
And well only tip I know of beside practice practice practice is using older decks that clump together a bit.
There's not really an upside to using fresh slippery cards for cuts or packet flourishes when you just start learning a new cut. I think you are making it harder on yourself by using a new deck. Ofc you will want to be able to have the skill to do it with a fresh deck obviously because it will look much cleaner in the end. But using older clumpy decks definitely makes the learning process easier.
But using a clumpy deck will not prepare you for the slipperiness of a new deck ofc, but it will give you more practice time to get the general mechanics down. After that you can learn with a fresh deck and get that fingerspitzengefühl down.
Yes, dry hands do hamper improvement a slight bit. Rub any normal lotion on your hands and you should be fine. But remember, too oily hands work as bad, so be careful with the amount of lotion.
Once you have it down, I guess it comes down to practice. It will just come, honestly. If cardistry was easy, everyone would be doing it. But they don't. Which means it is not. Any move requires a lot of practice.
As said above, clumpy decks do help. And there are some moves you HAVE to have poop decks, slippery decks just won't work (for a few packet flourishes atleast).
But it would improve your cardistry all over if you use new or even just a little bit worn out deck, not exactly a very clumpy one. Because your hands get better training.
And I don't feel that cardistry trainers help at all, just saying.
Just keep practising, it will happen one day that it will just click. Remember, cards are not supposed to be gripped to tightly (unless specifically mentioned). The cards are supposed to dance between your hands, not suffer some sort of torture.
Lastly, listen and watch tutorials very carefully. A good teacher always tells you when you have to grip the deck tightly or lightly. And pay a lot of attention to finger placements, correct finger placements may save your life some day.