Thank you for all the suggestions! I didn't expect to get so many suggestions. I think the first thing that I will try is getting a hollow tube to increase the tension on the bolt. Unfortunately a lot of the suggestions are not practical in this case due to the limited amount of space to extract the bolt, or due to cost concerns.

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And yes, I have tried to twist the stand instead of the bolt, but the issue is that the bolt is stuck in the stand itself, so twisting it simply twists the bolt without undoing anything.

Additionally, I have no power tools. If I did have any, the way I would go about it would be to grind the stand off, as anything else would not be able to work within the tight space.