Implementing the details in the inventory system turned out to be a pain in the ass for no reason other than my poor comprehension of the functionality. After hours of playing around, I'm happy with how it's working.

On top of the incrementing column, and it being able to tally the damage types (shown in the bottom right corner of the GIF), it can now continue to do all that while the player drags, rotates, and drops their items around. Obviously, I will need to block a player from doing this willy-nilly whenever they want, but hey, it's working, it's working!
So many small details in the functionality of this, I'm surprised how much code it took to get here. The small details include showing a semi-transparent preview of the item as you drag it, an overlay (for lack of a better word) that colors the tiles green if the item can fit and red when it cannot, and even accounting for which tile you are dragging on the item so that becomes its center of origin when rotating. Wild!