When a GM sets up a character sheet on the responsive site, there's two options they can choose between.
"Fixed Width, Word Wrap Off" and "Variable Width, Word Wrap On"
I tested out your sheet and noticed that the sheet as you posted it does not format correctly with the "Word wrap off" option chosen, but does with the "Word wrap on".
In message 243 of this thread:
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Jase talks about those options a bit.
You might try looking at that.
I tried different options and different tags/tag locations but couldn't get it any better than you got with the <pre> tag showing and the sheet formatted correctly.
Might be something obvious but that's getting overlooked, might be a bug. No idea.