I was playing with the inventory earlier. My goal was to move the controls into a wraper that could be moved around. this worked well, but I have some bugs im working out. Heres some of the ZO control children I found that may be of use.
The one I missed in the image is ZO_PlayerInventoryTabs
This was a big help in finding the control names.
http://wiki.esoui.com/Raw_globals_dump
note if your moving some of the existing controls many like to Anchor on the right hand side.
There is also 2 functions ZO_PlayerInventory_Initialize, and ZO_PlayerInventory_Initialized I found interesting but haven't completely figured out yet.
I hope that helps some.