This is more of a head cannon than a theory, but I want to contribute to the god tier discussion. My theory that karkat could use his blood powers like you said, using his blood as a weapon, but also he could control other people's blood. Make them move around like a puppet. Also since blood has to do with bonds, make others want to fight for him.

I also think that although karkat and anyone who didn’t go god tier wouldn’t get the just/heroic thing and clothing/flying abilities, they would get immortality. I just think once you claim the prize you’re immortal or something  

I am still not sure about you opening the door granting immortality, really. While weaponizing blood could maybe work like that, though, I heeeeeavily doubt Karkat would’ve used his powers to use others as puppets, merely because I don’t see him like the kind of person to do that if it makes sense? He did make a bond with Jack and add him to the team to fight alongside him though.