My theory was that zahard and co did not originally enter the tower to rule it. Rather they went there with some sort of mission. Then given the chance at immortality the heads, except v, chose to take it. And then zahard blocked of access to the next floor in order to prevent anyone from completing the original quest. Arlen and v objected to that and hence the war between them. Odds are there also were other reasons why they didn't advance further that played a part into this, hence why it seems like the war between heads didn't start the moment they stopped climbing.
I am also thinking there is a chance that v was the person who was to become king but then zahard merely got ahead of them and got the contract instead. And this builds to my other crackpot theory, since zhard got the kingship contract earlier it is at risks if someone climbs higher than him, hence another reason why he closed the door to the next floor and threw the key away.