This morning I just had to forgive myself for my imperfections.
I’ve been practicing Ardha Chandrasana (half moon) against the wall for most of this year, due to arthritic and wobbly knees. Now I’m much stronger, so I’m trying to practice in the middle of the room again.
I did fine on the right side, but I could not stay up on the left. I did all the little helpful tricks – kept my eyes focused on a single spot on the floor, didn’t try to turn my head up, put the block out to the side a little bit, paid careful attention to the strength in my standing leg, turned my hips parallel to the wall instead of the floor, but no joy. I just kept falling over. Finally, I went to the wall.
On the plus side, I’m also practicing Vrksasana (tree) in the middle of the room, and I can do that one.
I always try to come down out of the pose consciously rather than falling out of it. If I do fall, I go back up just long enough to come down carefully.
Practice Notes 
This might not help, but maybe worth a try if you’re not already doing it: before going into Trikonasana preparatory to going into Ardha Chandrasana, suck up the perineum with a moderately strong contraction and draw in the lower abdomen. Then as you go through Trik and into A. Ch., focus on the very center line of your trunk and head, from perineum through the top of the head. This is the Sushumna nadi. Radiate like a starfish from that center line–lots of energy and intention in the spreading action. Of course the trick, as always, is to not let go of all the other actions you described, as they are crucial–especially the standing-leg thigh and hip actions.