Another lead-up drill for Straddle Press Handstand is One Leg Press Handstand, a drill #7.
As you can see, in this drill you’ll kick-up into a freestanding handstand while lowering only one leg and keeping the other one in the air. By staying in that balanced position, you’ll increase your dynamic flexibility. Initially, you’ll only be able to lower one of your legs just a bit before coming back up. After a certain amount of practice you’ll succeed in touching the ground with that leg and come back up without the kick-up.
As you can see in the video, that bottom range of motion is still a bit difficult for me and I had to use little momentum in order to come back up. Even though I only started practicing this drill recently, it’s a great one. By using only one leg, you’re basically learning to control your entire bodyweight in that dynamic manner, which is essential for performing the straddle press handstand.