Hehe I must say I did have a bit of luck there and throughout the entire conflict with Caelum and Yomi.
The "timing" was meant to correspond with an attempt to surround the capitol and fear rout most of the army there. Prince of Death had taken a beating the last time he tried to solo the province and was regaining strength in high dominion and rearming with better magic items. I didn't think he would necessarily win and if in trouble retreat to an open province, but as you have written he got lucky and only faced provincial defense.
When Caelum started the invasion I was in a bind because if I was to meet that threat it would leave my southwestern flank exposed. Thinking other nations might be involved I park an army nearby Yomi and offer gold, gems, items or land to stay neutral or agree to a NAP. He refused because there were no independent provinces left and proceeds to attack the next turn. I lose some land to Yomi, Mictlan attacks and takes a province, and Caelum keeps marching toward the my capital.
I go into turtle mode since most of my army is pinned down defending key provinces. I finish building a fort in one area freeing up those defenders and get a random event creating another in a wasteland near Caelum. I love maxed luck scale
Ulm goes on the counterattack. Caelum retreats to the capital pinning down his army. I then flank Yomi from his south through Caelum's former territory. This breaks a stalemate forcing Yomi to attack a well defended position.
Ulm goes on the counterattack. Captures Yomi's capital and remaining provinces. That army is now free to march on Caelum. After much wailing and gnashing of teeth along with about a hundred ulmish casualties in the final assault, Caelum was felled.