I could never balance a freestanding handstand as a gymnast unless I was on pbars/parallettes. I started practicing on and off on the floor a few years ago and now I'm up to a minute and a half with no walking! I try to do a minute freestanding daily.
What helped me most:
1. Holding split, double stag, or L-Handstands
this lowers you to the ground and makes finding your balance point easier
I didn't switch to straight handstands until I had a minute in split position, and the transition was seamless (The first day I tried straight handstand I was able to reach a minute).
2. Keeping the balance towards your fingertips
This will fatigue your forearms faster, but at least for me it's way easier to find my balance point
When I lose my balance, I go back to my fingertips until I've regained balance. Then I try to shift to the center of my hand so I don't have to grip as hard.
3. Shoulders raised + straight elbows
To hold for a long time you want to keep balance-checks to a minimum, and in the hands ideally.
If you have multiple sources of balance-checks (shoulder angle, shoulder level, elbow bending, back movement, knees), they compound and make regaining balance difficult.
4. Use the wall
The wall is a great tool for handstands, here are it's best uses IMO:
-Increasing your endurance by going for new records
-Alignment with your belly facing the wall (walls are straight, so more body contacting the wall = straighter body)
-Applying alignment to free standing by gently pressing off the wall repeatedly to attempt at finding your balance point
Hope some of this helps
