How should I frame my transition from an unsafe situation as I apply to other universities, pre-tenure?
Your personal circumstances should not affect your attractiveness as a candidate.
People move for personal reasons all the time: spouses getting better jobs elsewhere, proximity to better medical care or schools for their kids, less taxes, affordable housing, or because the weather sucks where they are now (shoutout to the British Isles!).
This question may arise in personal conversations when you interview, but should not be a factor (or even mentioned) in your application materials.
If your department head is supportive and your move is motivated purely by personal reasons, then you should have them write a letter.
I would advise against getting into details that may present your current institution in a negative light. Interviewers like candidates who present themselves as team players. Statements like “the university put me in a situation that threatened my health” may come across badly. Try to word it a bit more gently: “I heard that prospective institute name has excellent healthcare and this is a factor in my decision”.
Good luck!