See if it's any easier now.
I didn't bother with the mat, but I still placed the cushion on the floor. Now I expected to be able to get up on the first go. Mistaken. It still took me 4 or 5 goes before I got up to the wall, and the hesitation isn't completely gone. But I have the reference that I've done it, so the fear is not debilitating.
Once I got up, I managed to hold for 30 seconds - I was able to focus on my posture so the weight came over my shoulders and not so much on my wrists and arms. My second attempt I held for 20 seconds. And the third for 20 seconds, but I tried to dip a little, to feel how the strain is on my arms.
I'm a long way off pushups yet, but I can do handstands. Hoorah! When I'm strong enough to actually do pushups, I should also be able to get into position without the run-up... at least that's what I hope to be able to do.
Third day at this...
I can get up now fairly easy - it is a combination of enough momentum and the right technique... and putting your hands in the right place - too close to the wall and you bounce off, too far away and you won't reach it (or fall backwards onto it).
I trust my arms to hold me now, so I don't need the cushion. Most of the strain I still feel on my wrists - but it's a good training for them.
I tried widening my arms-width to see if I had more stability, but that was a no no. Maybe later when my arms are even stronger, this could make the dips and pushups easier, but for the moment I need my arms under my shoulders to hold my weight.
I held for 15 seconds each stand (3 stands), and did some very small dips of a couple cm. It's a start.
New info... new technique. I still keep forgetting that the internet has info on everything, and then I surprise myself when I suddenly think... "Oh yeah... I can look that up on the internet!!!"
So I looked up "handstand pushup" and found a video that shows another way to get up into the handstand position. Instead of the flipping, as I've been doing... with this technique you stand on all fours with your head away from the wall, then you put your feet against the wall and walk up, moving your hands closer to the wall the higher your feet go. You end up in a handstand with your face "facing" the wall, instead of the back of your head.
This is a much easier technique, and you already get to do a little walking with your arms, so the pushup doesn't seem so impossible.
What a difference a day makes... and a good technique. I can get up to a handstand easily now, using the technique above - it doesn't shock the system too much. And having to "walk" yourself closer to the wall helps your confidence while already giving your arms a good workout.
I did this twice with a three minute break inbetween - on the second go I even managed a couple of half-pushups. So I'm almost there. I'd like to be able to do at least 5 full pushups before I consider this project successful. And when I've reached this goal, I'll post a video as proof