FWIW, there are two things that really helped with balancing in the pose, for me.
One is a weird-sounding bit of advice I found somewhere to point your perineum at the ground. Which makes sense when you try it -- if your pelvis is tipping over to one side (or front or back), that automatically unbalances you.
The other thing I find is that the higher I can get my leg, the easier it is to balance, especially when taking the leg to the side, because I can stand up straighter; I'm not leaning forwards in order to be able to reach my foot.
So if there's some room for your hamstrings to relax a bit more, working on that (maybe in the reclining version of the pose) may make balancing a lot easier.
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One is a weird-sounding bit of advice I found somewhere to point your perineum at the ground. Which makes sense when you try it -- if your pelvis is tipping over to one side (or front or back), that automatically unbalances you.
The other thing I find is that the higher I can get my leg, the easier it is to balance, especially when taking the leg to the side, because I can stand up straighter; I'm not leaning forwards in order to be able to reach my foot.
So if there's some room for your hamstrings to relax a bit more, working on that (maybe in the reclining version of the pose) may make balancing a lot easier.