I apologize because I know your a big deal Zuberi, but respectfully,
Chant of Rage says "it must move towards a creature with a hate token, if possible" This card doesn't specifically say only one time. It dictates, that if the target can move towards the hate token, it MUST. So even a non-fast creature would double move to reach the hate token as long it wasn't hindered, furthermore if that creature was fast, it is required to make a melee attack, because, "During its activation, the enchanted creature MUST melee attack a creature with a hate token.".
I understand the only way around this is by choosing another MUST, like another creature with a hate token, or a wounded creature if the target has Bloodthirsty X, or a taunt.
The portion you added about not having to make a mandatory action possible has more to do with tanglevines, rooted plants, and the Blue Gremlin not being forced to pay mana to teleport through a wall.
In this case, all the mandatory actions are possible, and are required by song of hate, so the Griffin must move twice and attack the crocodile.