I was unaware of ShowGiftMenu as well...does it take the actor's carry weight into account? If so, I may have to edit some scripts.
It looks to me like it's the same inventory with additional options for making it only way way - from the player, or to the player. So I imagine, but haven't tested, that the item weights and encumbrance would be the same.
Now that I have this working, here's a full example:
Show Gift Window and Track Items Given
This is used for the Player to feed his animal companion. The FormList is created in the CK and includes all the food (Potion & Ingredient) items I want to consider food for the animal.
http://www.creationkit.com/Complete_Example_Scripts#Show_Gift_Window_and_Track_Items_Given