I can't disagree. However, do you think if we approached it only from the theoretical grammar's point of view "living" wouldn't be the right option here?
Perhaps I used the wrong expression with 'theoretical grammar'. I think that the prescriptive grammarian would insist on 'having lived' - and that's almost certainly what I would say. However, (personal opinion only), I think that only a pedant would object strongly to 'living'.
If the speaker had actually moved elsewhere and returned for some occasion, then s/he would almost certainly say only "Having lived here (for) most of my life, ...". In that context, 'living' would be less acceptable.