I got the axes working using the two-float method, but there's no cooldown for them, where you can't use them to attack for another second or two as with vanilla tools. I was wondering if there was some way to get my axes to have the same cooldown as vanilla axes?

 

EDIT: Also, specifically, what are the two floats for? One's for the damage, but what "speed" is the second float for?

I'm pretty sure speed is the recovery time mainly what this thread is asking to fix.

Do you mean attackspeed? You could override getAttributeModifiers in your Item class

 

@Override
public Multimap<String, AttributeModifier> getAttributeModifiers(EntityEquipmentSlot equipmentSlot, ItemStack stack) {
    Multimap<String, AttributeModifier> multimap = super.getAttributeModifiers(equipmentSlot, stack)
    multimap.put(SharedMonsterAttributes.ATTACK_SPEED.getAttributeUnlocalizedName(), new AttributeModifier(ATTACK_SPEED_MODIFIER, "Tool modifier", attackSpeed, 0));
    return multimap;
}

Do you mean attackspeed? You could override getAttributeModifiers in your Item class

 

@Override
public Multimap<String, AttributeModifier> getAttributeModifiers(EntityEquipmentSlot equipmentSlot, ItemStack stack) {
    Multimap<String, AttributeModifier> multimap = super.getAttributeModifiers(equipmentSlot, stack)
    multimap.put(SharedMonsterAttributes.ATTACK_SPEED.getAttributeUnlocalizedName(), new AttributeModifier(ATTACK_SPEED_MODIFIER, "Tool modifier", attackSpeed, 0));
    return multimap;
}

Thanks for the suggestion but I figured out my problem. The float value is actually 4 above what it is in game. For everybody wondering, to get the default Diamond Axe attack speed of 1, you must put -3F into the second float.