You dont die when cauterize procs, you get your health back to 40% and the debuff when your hp hits 0, so no repair costs.
Btw i always save ice block for cauterize, it removes the debuff so i dont need a healer immediatly after. Maybe bandage or evocate (glyph) when necessary.
For messy AOE or other aggro related problems i use invis, the 3 sec fade time is short enough and usually in the first "tick" of invis the mobs / boss go back to the tank anyway.