Here's the actual climb in question, according to OP.
So if you are out of the saddle, clipped into pedals, and have your hips to the stem and are bending forward at the waist, then there's little more you can do to balance the bike.
Consider not wearing a backpack.
You might be able to vary your track on the path by zigzagging, or taking a slightly less head-on approach.
Try the climb again, while recording on strava. Then use the Compare function, or a link like this https://www.strava.com/segments/4354748/compare/MzU0NzM3Nzc4NSwxNTgzODc4OTU0NA==
to compare your best segment effort to someone else's. The top time was only doing 1.4 km/h on the really steep bit at 0.7 km into the segment.
Generally the answer is momentum, and lots of it. And if you stop, you're stuck.
If you're there, try and watch other people ride the same track. See how they approach the same sections and where they push hard.