@east81 I found it very helpful to re-orient myself and do handstands with my back to the wall. I only switched to this after I was able to consistently hold 3x60seconds of full handstand. This simple rotation meant I was much more able to practice kicking into handstand, and I just found it easier to move my feet away from the wall this way than when facing it. You mention needing to spend time upside down. Between months of handstand work, and moving to face away from the wall, I finally noticed a swithc in the way I hold myself. I can finally correct my balance and often come back into my handstand rather than falling out as I used to.
I'm seven months in and just this week, for the first time, I was able to kick into handstand and stay, tho only for five seconds. I'm also pushing past 20seconds on my 100% freestanding handstand now.
Thanks for the tips, OP. I train a slow descent on my last five seconds of each hold, but you've inspired me to really start pushing into handstand, and to more fully embrace handstand push-ups.