one of the reason that your player gain skill slowly was becoz they gain star.
If I not wrong, when u bought these players, they gained star in few days after u bought them, am I right?
After that, they gained skill very slowly after training. So, when they reach nxt lvl, their star will drop, then they will progress faster.
You may have to buy 2 or 3 new players in nxt league to strengthen ur squad to compete in new league.
Most of the time, i dont assign skill of my backup players, so they can progress faster. I only assign skill when I need them.

Hope it can help u.