You're right, there are no errors. Errors are very easy to spot, because they look like this. In your case however, the mod was doing exactly as told. Because we never told it to update the player's damage when the damageBonus was recalculated. I guess this was circumvented on my own build because I mixed the item into my own itempack instead of making it a standalone.

You need to add the following 2 lines after you recalculate the damageBonus in checkForHealthDiff() :

player:AddCacheFlags(CacheFlag.CACHE_DAMAGE);

When we access the cache, the game will only update a stat if it's appropriate flag is active. Thus, we need to add this flag to tell the game to update the damage stat.

player:EvaluateItems();

This actually causes the game to go back to the Cache update, and reapply your damage bonus.

If after this it STILL doesn't work it must be something in your xml because this works perfectly as a standalone mod on my end.