@The:
I'm…going to jump aboard the bandwagon of people saying Kaido(u) use to be a very high-ranking member of the Marines. In fact, I'll go as far to say that Kaido(u) was an Admiral at the same time Zephyr (Master Z) from Film Z was or a Fleet Admiral after the-now Commander-in-Chief Kong. It would be funny really. One former Admiral (Zephyr) turned into an extreme vigilante/Pirate-hater, and another former Admiral (or Fleet Admiral; Kaido) turned into the complete opposite.
I don't think it's a coincidence that X. Drake, a former Rear Admiral of the Marines, targeted Yonko Kaido(u) specifically. I also don't think it's a coincidence that the "old marine song" Zephyr and others sung in Film Z roughly translates to 'Kaidou' (according to 75% of the people uploading the OST track to youtube.com and other sites). Kaido(u) is bound to be an older man (age 50+) as well. And yes, I know it's spelt Kaido.
Could it be a coincidence? Yes. But right now, I don't think so. Though I'm sure I'll get flak from some for jumping on board the 'Kaido = Marine turned Pirate' wagon. lol
So… are you saying that prime Moria was Admiral level, since he ans Kaidou used to fight equally? Then something happened and Moria got crushed?
If anything, the Admirals at the time were most likely Z, Sengoku and Kong. Kong gets promotion, Z quits and Sengoku is left as the only Admiral.