What stretches are most helpful for my HS?

Working my wall HS for time twice per week; just added some shoulder weaving at the last practice. Two days before that practice, though, filmed this "test run" of my free HS.

I have been working on various mobility limitations (particularly in the T-spine/shoulder girdle, though unsure where exactly, and hip flexors) for the last year, but what stretches will give the biggest payoff for straightening out my HS?

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none if you don't understand what the correct position feels like. Just being flexible is not enough, I've seen people who had contortionist level flexibility who still did typical closed shoulder handstands because they didn't grasp the specific feeling of the alignment.

Typical shoulder stretches, bridge, and splits all help. However, until you know what it feels like to open your shoulders and pull in your ribs under load the stretching will not help you that much.

Now once you start to understand the position and see that you have a restriction because of your flexibility, then the stretching will be a lot more potent.

Yuri, thanks for the reply, and note about feeling out the form. I have only recently brought chest-to-wall wall HS back into my program, after spending time opening my shoulders with stick dislocates & OH squats. I have felt the position, and practice the hollow body supine on the floor between pull-up sets (not on the BtGB program, but working largely on MU & OAP progressions for strength), but have incredible difficulty moving into it when free. I know spending time in the wall HS will help (which I am doing), but hope for some stretches to most effectively address places I know to be tight/weak.

The gymnastics club at Texas Tech worked with me on this and mentioned the same points you did above before I moved, but it has been a few months since I worked it specifically.

also, keep in mind that handstand is a specific element. Most hand balancers or gymnasts probably can't do a good overhead squat while most olympic lifters will have trouble getting into an open shoulder handstand

The most effective stretches are the ones that specifically relate to the intended skill

OK, so my simple answer is to work the wall HS, which I should have known. I would assume chest-to-wall and working closer over time. That said, which supplemental stretches will be most beneficial? My program used to include bridges, but I am prone to doing too much: is bridging the best supplemental stretch or something else?

Handbridging and cat stretch work that shoulder flexion.

It is also improper IMO to start with a HS without the arms already by the ears. Especially in beginners since they will tend not to open the shoulders upon contact with the floor.

It's fine for gymnasts with a basic grasp of open shoulders but again inappropriate for anyone else.