Thank you for your comments, some interesting comments here.
I did not consider the D810 or D850, they are significantly heavier than my D600 and slightly bigger too. I prefer to use a smaller, lighter camera, although there is no doubt the D8xx cameras are outstanding.
The D750 is an interesting option I had not considered. It is the same size and even marginally lighter than the D600. The tilt out screen would be useful, and newer EXPEED processor should give improved high ISO performance. Although I don't have many AF lenses the wider spread of AF points would be useful even for manual focusing. The D780 is rather expensive right now but could also be an option.
The Z6 is probably my first option among the mirrorless cameras. Maybe the Z5 would be better since it accepts SD cards, but the EVF is lower resolution and the it does not have a BSI sensor so high-ISO performance is not as good (not that I shoot at high ISO often, but having more head-room would be useful).
On the other hand, another option would be to expand my m4/3 kit ...