To be honest I see Moria as an ambitious character that will mever serve willingly under other people, he is (or better was in his prime) a lot like Luffy before he was broken but that just filled him with anger. Then the most likely choice would be BM since they think alike to an extent (they are both evil, hate Kaido) maybe he would have been attrcted by her if she did some overwhelming display of power, he understood she was too strong and that Kaido too reached that level so it was good, and even better if there was no other choice like with BB, to ally with her. But it would be an alliance, or better servitude, like Bege woth BM or even BM and Kaido with Rocks or the BB lvl 6 crew and BB himself.
Shanks and WB simply wouldn't want a post wreckage Moria woth them (even because he got lazy and took as his motto "make me pirate king" aka you work for me and my dream while i take a nap).
Yet in the end he didn't choose any yonko but instead choose the navy. Maybe because it provided him the protection from Kaido he needed to build up his power again and even more tale ships and do horrible stuff to people in the Florian triangle (aka WG please close an eye and I will fight for you and at the same time increase my power). Yet he didn't do the calc right and was wrecked by paradise Luffy.