QUICK UPDATE:

United is paying me everything.... I was quite surprised, actually.

They gave me the "We have signed the Montreal Convention and therefore will only pay you a ridiculously low amount of what was stolen" speech, but then they said "But since you fly so much with us, we have decided to offer you a full refund".

Anyway, not as much pain as I thought I would get.

I am happy.

In case you are wondering... the refund will be something around USD 4kish....