The jump rope part of White Buddha was also the most difficult part for me to learn. For me, these thoughts were helpful.
Keep the yoyo close to your throw hand. If it’s centered in the triangle of string then it can move forward or backwards more and I’ll miss landing the jump rope move. This made the biggest difference.
I was making the jump rope “loop” motion too large by bringing the string too close to my body. I was “over looping” that is, moving past the yoyo and missing the landing. It’s a much smaller motion than you think.