Honestly, for the Earth Kingdom the solution might be Bumi stepping up to take a more prominent role in organizing what's going on in the south... and presumably also finding a successor because he's fucking old.
Bumi has, per Granite's musings on the discord, been pulling his weight in the south for 100 years. Indeed, this has been a major cause for discord in Ba Sing Se, and they probably only supported Bumi when things were at their most dire, because after all, who wants a more independant and self-reliant Omashu?
We don't know a lot about the last 100 years of Earth Kings, but when Sozin ascended to his throne, his opposite upon the Jade Throne of Ba Sing Se was the infamous Jialun, a man whose first recorded acts were to purge the intelligentsia established by Avatar Kiyoshi, and turn the Dai Lee into what it is today, a secret police force that thinks nothing of disappearing people, brainwashing, and controlling the modern Earth Kingdom through puppets. He also saw little wrong with Sozin's ambition, since he too was ambitious, and claimed many of the same islands that Sozin would later use as the jumping-off points for the invasion. Jialun's actions were probably one of the major reasons that the Earth Kingdom lost as much ground as it did. Since the days of Jialun, there seems to have been some change in the appointment of Earth Kings, with at least 3-4 cycling through the office since his time. Kue, famously, was placed on the throne at the age of four, and was entirely a puppet of the Dai Lee. But none of those kings, none at all, bear as much blame for ruin and destruction as Jialun.
My hypothetical line of descent goes
46th Earth King (260-231 BG)
47th Earth King (231-160 BG)
48th Earth King (160 BG-110 BG)
Jialun (110 BG-25 BG)
50th Earth King (25BG-2 AG)
31st Earth Queen (3 AG-52 AG)
51st Earth King (52AG-80 AG)
Kuei (80 AG- Now)
Or to put it differently, the last 150 years have seen the Earth Kingdom ruled by:
- Caligula
- Queen Ranavalona
- Tsar Nicholas II
- Prince Regent George IV