i wanted to chime in but have not tried the 24-240 so the following is hot air.
Better a smaller sensor bridge cam like the rx10 or the panny for less than the weight of the 24-240. My hunch is that it would be a fair bit sharper too (not really checked this out to be fair). I guess I just thk that it is a waste to use a jack of all trade/meh lens, though undeniably versatile) lens on such cameras. Why bother wasting all that detail.
Other options which would be smaller and probably sharper would be a micro 4/3 or aps-c two lens combo.