How about, going by seniority as Head of State?
That would ensure rotation (a newly inheriting Crown Prince/ss would start below elected Presidents, a monarch of another country would take over), but also make it unlikely for anyone but a monarch to lead EU (with 5 Kings/Queens in EU after Brexit and 1 Grand Duke, the senior living monarch of the 6 is likely to outrank all the 21 Presidents at any time).
The present EU order of precedence (as yet including Ukogbani) begins:
1)Elizabeth II - 1952
2)Margrethe II - 1972
3)Carl XVI - 1973
4)Henri - 2000
5)Grybauskaite - 2009
6)Higgins - 2011
7)Niinistö - March 2012
8)Ader - May 2012
9)Pahor - December 2012
10)Anastasiades - February 2013
11)Zeman - March 2013
12)Willem-Alexander - April 2013
13)Philippe - July 2013
Does the fact of EU capital being in Brussels commonly make Philippe rather than Elizabeth the highest ranking person in Europe, by fact of being the host Head of State? What are the EU obligations of Philippe?