Similar to your experience,
there is a thread on the UA forum, that mentions mechanics taking seats apart "until they had to turn the plane around", and other stories. Unfortunately, nobody in the thread reported success.
Good luck - even homeowners policies often have exclusions on electronics unless they are covered (like cameras and other electronics) on a separate personal articles policy. Not to mention the deductible and possible loss of a claim-free discount would be way more than even the most expensive phone. Only, to my knowledge, the expensive insurance from the cellular companies covers theft and loss. Third parties like Squaretrade and Applecare only cover physical damage.
The worst thing to me, when I left my phone behind on a plane, was the loss of photos and data. Catch-22 in my case, as I had avoided using my pockets in flight, so it didn't fall into the seat, but rather I stupidly left it in a bin.