Mick, as ever you are a man of sense. I expect, and it has been discussed on other threads, that many people are sensitive to other people's 'signature' songs when that person is present, as a matter of graciousness, but agree there is no reason not to perform them in general. And of course claiming all of X's songs were 'signature' songs is silly.
I am still hoping for other suggestions for dealing with the musicians from whom the family member extracted some sort of 'promise' not to sing them and not to do 'tribute' material (very weird, to my mind). I suspect time is on our side.