I did try pull ups but he is a very heavy wetter and nowhere near dry so they weren't absorbent enough and I returned to using nappies.
In the past he'd always worn disposables but I recently got some terry squares cheap and have been using them ever since. They work well but he resists having a terry put on when a disposable didn't bother him.
I wonder if it is taking longer to put the terries and wraps on than a disposable would. Have you considered using pockets? I know some people have done the poppers up on the widest setting so their child can step into them like pants and then they tighten them up whilst the child is stood up.