Lots of wall HS for time. 10, 20, 30, 60, 90. Basically create a really strong shoulder girdle.
HS back against wall, slow press down. Focus on lowering in straddle as slow as possible, as low as possible. Find out the point where you can then press/pull your back to HS against wall. 10 or 20 of these.
Press Headstand on floor in straddle then pike. Then elevate your head onto a few layers of a panel mat and practice it. This is mainly to build the lower back and core strength to lift your legs.
Lots of straddle hip flexor activation drills like straddle L holds.
BHS drills should be limited to strength and flexibility work. Back walkovers, limbers, kickovers. Leg lifts and v-ups.
Kick to arched handstand against wall, snap down to pushup position.
More HS work, free and off the wall.
Leg strength like squats, squat jump. 1/4 squat to jump as high as possible. Lunges and single leg squatting and jumping.
Arch rockers are reverse leg lifts ( like where you hang on a vault or pommel horse and lift your legs- however Headstand leg lifts work the same thing and are harder ).