That's a very nice theory, and I admit I would be absolutely mind-blown if Isayama takes that direction.

However, the chronology on which you based your math is wrong. First, for reasons unknown to me (does anyone know?), the calendar in AoT is the age of Eldia minus 1000 years. So for instance, in 840, when the story begins, Eldia is 1840 years old.

Let's admit the time-loop is 2000 years long: the end of it doesn't match with the supposed death of Historia. In chapter 86, it occurred to me that Ymir's reign begins 1820 years FROM the moment Grisha is being told the story by his father (Year 820 i guess). If the ethnical cleansing lasted 1700 years, it means it stoped 120 years before that. Still according to Grisha's father, the war ended 80 years in the past, the same period of time of the 145th. So 820-120= 700. So the ethnical cleansing stoped before the 145th, who reigned around 740 , and way before Historia's reign. Your mistake was assuming that each king reigned exactly 13 years until the 145th which is wrong if you do the maths: 1760 (age of Eldia at the moment of his reign)/13= 135,615.... But this isn't the case since 145 kings already passed since that, and not 135. Another way of saying that: let's assume there was 145 kings who reigned 13 years exactly: 145x13= 1885. That brings year 885 whereas it's barely year 850 in the present events in the manga. Now let's assume that every king AFTER 145th reigns exactly 13 years (and that was also the case of Frieda Reiss by pure coincidence). 240 years remains before the end of the timeloop (2000-1760). This means 18,4615... kings remain (240/13) and not 8 as you said. That means 18 kings will reign 13 years, and the last one, the 19th, will reign only 6 years (0,4615... x 13).

So to sum up:

Year 0: Ymir's reign Year 1700: and of the ethnical cleansing Year 1760: 145th king Year 1840: Beginning of the story Year 1845: Beginning of Historia's reign Year 2000: Death of the supposed 164th king

Maybe I misunderstood something in your post, if so correct me ^{^} I still like your explanation of the time-loop very much and I'm sure we can find a way to make the it match with the events somehow.