I assume you're having trouble with the weight that is being put on the elbow in the compressed/flexed position when you go through the transition.
That's totally normal for a lot of people when first learning the move. It doesn't bother me now, but can easily be produced in almost anyone if you weight muscle ups enough.
Basically what you want to do is strengthen the heck out of your forearms, triceps, and biceps (aka all the muscles that connect in and around the elbow).
Rice bucket works well for forearms -- although you can do whatever you want for this.
Biceps are definitely hit well in supinated back lever as well as some planching variations (hands backwards, sideways, rings), pullup variations, etc.
Triceps are hit well through stuff you already know. Dips, manna, HSPUs, etc.
Basically, just get stronger in the arms and it tends to go away. You may need some specific isolation work or you can emphasize more compound movement strength in your routines.