An option that you haven't weighed, apparently, is to treat your iPhone like a woman, with care and respect.
"have never had trouble keeping my phone from harm"
You lost 3 iPhones within a year, due to theft and misuse. Your belief that you "never had trouble keeping my phone from harm" simply isn't true.
"if one of my family members is aware, can I file a claim under their number and get a phone?"
No, of course not. That would be considered fraud. I'm sure that Asurion agrees with me.