That is his life goal in this new life of his though. He was overworked, so he really wouldn't go around turning stones to find a rebel group.
The authorities can't be handled that easily either. Let us say that there are records where would he present that?
The guild? They have strong adventurers but they can't really dip their fingers if the enemy is on the political side. It's out of their jurisdiction if that happens. If it's not then from the previous chapters, it shows they are a couple of steps behind the enemy, not to mention they are infiltrated.
The king? They probably already know about the group and can't squash them easily(huge long legacy clan/rich nobles/probably a foreign force from another kingdom) or part of the group itself.
If it's the former then that means the members have enough influence that if they just kill them off there would be subsequent problems that would follow. If it's the later then he has to take on a kingdom.
Also while they are taking care of the organization, who can say that the other kingdoms won't take the chance to attack them while they are busy dealing with internal strife?
It's a long term project to attack them.