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I would consider using this topic as a personal statement instead of a diversity statement, because it'll allow you to go in greater depth about the topic. In addition, you can use it to show character/strength as well as (very) strong softs. I think this could be a really strong PS. I've heard of admissions' committees looking over PSs but not necessarily reading DSs.

Does your PS add more to your likelihood of getting accepted than this? If not, I'd use the opportunity to use this as a PS and be able to explain the topic more extensively.

Which schools don't read diversity statements ? It seems that personal statements might be given a quick read while diversity statements get read & often redirected.

OP: Detailing your problems may harm your chances of admission if it seems likely to render you, even temporarily, incapable of coping with the work demands & pressures of law school. Problems breathing & debilitating headaches suggests that potential emergency medical concerns may be warranted. I realize that you specified the trigger as any moderate level of physical activity, but I'm not sure that readers will get past the idea of breathing difficulties & debilitating headaches in addition to suffering pain.

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Otherwise your DS seems quite compelling & well written.