How do Battlemage buff and Battlemage's Cry interact?

Battlemage buff says "Gain Added Spell Damage equal to the Damage of Your Main Hand Weapon"
and Battlemage's Cry says "Increases and Reductions to Spell Damage also apply to Attacks at 25% of their value per 5 power, up to a maximum of 150%".

What seems to me like what would happen is you always have the extra spell damage when you have the Battlemage buff, but your weapon attack is just base, and then when you go to attack the Battlemage's Cry causes the attack to take that Spell Damage value into account (this means multiplying your effective weapon damage by up to 2.5x), but can anybody confirm who uses these together?

Between using an elemental strike as the main attack and things like Iron Will, this seems like a lot of ways to double-count damage stats. I am new but it seems like adding Shockwave support to attacks is really popular right now, which is along the same lines.

The two don't interact. Battlemage only adds damage to spells based on the flat damage stats on your weapon. Any other modifiers, such as to attack damage from Battlemage's Cry, have no impact. And "increases and reductions to spell damage" does not include added damage (or more, or extra), so that added spell damage from Battlemage does not get applied to Battlemage's Cry's effect (and hence can't be applied back to your attack damage).

Ok, so I think I understand now. Battlemage adds flat physical damage to spells, but what about Iron Will passive? Seems that works as % incrwased spell damage so should allow you to double count your str bonus on attacks.