So this is a typical gauntlet? Meaning no heals? Or are they healed/armies replenished in between rounds? I’ll assume the latter.
Round 1 : Gyou'un and Chou Ga Ryuu
The Heavenly Kings are already getting pushed to high/extreme diff. Gyou’Un’s Great General level offense will prove unstoppable to every HK bar Kaishibou, and even then, the Raigoku should take care of him. Chou Garyuu’s great tactics and defensive mindset will ensure that he and Gyou’Un wait until the exact perfect moment to strike, and when they do, Heavenly King heads will go flying.
However, I do think the Heavenly Kings will be smart enough to not engage Gyou’Un directly, and will instead try to fight him at a distance/utilize strategic retreats to attempt to trap him. Kyou’En in particular is going to be very dangerous, if Gyou’Un gets baited by him then the big G is going to lose his life very quickly.
So this war is going to be a test of each’s sides ability to bait their enemy into exposing themselves, and then using a lightning fast offense to slay them. The HK will be better at laying the bait due to Genpo/Rinko/Kyou’En, but the RSJ duo will be better at unleashing that offense due to Gyou’Un.
I’ll say the HK win just due to being more versatile.
Round 2 : Kisui, Batei and Ryuu Tou
The Heavenly Kings mid diff. Kisui, Batei, and Ryuutou are really all one trick ponies, and they aren’t that spectacular at what they can do. Kisui is strong at raising the Rigan Army’s Morale, but we’ve seen better morale raisers. Batei is a strong warrior, but we’ve seen stronger. Ryuutou is a tricky strategist, but we’ve seen trickier. Literally nothing these 3 can muster is capable of overwhelming the Heavenly Kings, and they’d be lucky to slay even one of them. Imo.
Round 3 : Bananji, Shun sui ji, Earl Rai and Earl kou.
The Heavenly Kings high/extreme diff. Bananji = Kaishibou as a warrior, and Shunsuiju is one of the aforementioned “trickier strategists” than Ryuutou. Earl Rai and Earl Kou’s tactics should theoretically be unbeatable to the HK tactically, though I’d be interested to see what Genpou would do against them.
Not much else to say here. I feel the HK would win but I’m not quite sure why. I think Earl Rai and Earl Kou are the weak links, Rinko’s Rindou is going to F their army up, I doubt they can counter that tactic, and Kyou En is going to be able to pick them off like flies. Plus Kyou En’s Army is faster than a standard army due to the speed with which he issued commands due to his archery, I’m sure that could play a pretty big factor.
Round 4 : Akou, Makou, Denrimi, and Sou'Ou.
This Heavenly Kings high diff. I think Akou is overall more versatile than anyone here, his fighting ability should be on par with Kaishibou, his offensive formations should only lose out to Rinko, and his defensive formations are very strong but Rinko can break them. Makou might be a slightly weaker version of Akou.
Sou’Ou and Denrimi are probably the weak links here. Denrimi seems to be a strong tactician, but Genpou is stronger. Sou’Ou seems to be a pretty impressive warrior and maybe even an instinctual, but his abilities are still pretty unknown, and he is overall weaker than Denrimi. I see Ousen’s lads giving the HK some trouble but ultimately the HK are going to pull out the win.
Round 5 : Tou, Rokuomi, Rin Bou, Dou Kin and Kan Ou.
Hmm...this one is very tough. Unlike all of the previous matchups, Tou legit has no weakness that can be exploited, he is overall just an extremely strong General who knows where, when, and how to utilize his men. The Heavenly Kings are similar, but it’s tough to say how this one would go. Extreme diff either way?
And last round : the right army generals of the Shukai plains : Gyou'un, Chou Ga Ryuu, Bananji and Gaku Ei.
Gyou’Un and Chou Garyuu alone are already capable of giving the Heavenly Kings an extreme diff fight, add in Bananji alone and the scales get tipped. Another Kaishobou tier warrior who also has some good battle sense and instincts, and that’s about all it takes imo.