Efficient Algorithm - Comparing lists with Virtual Scrolling

Question

I need to test an application through UI where there are two panels. One being available items and the other is selected items These panes can contain thousands of items

Each available item has a checkbox used to select it and then the add button will add it to the selected pane.

My problem is there is virtual scrolling implemented on the panels. Meaning I can only ever access a maximum of 16 items at a time, (I've tried scrolling down to the bottom - but still, css selectors only work for the items I can see on the screen)

My Question is what is the best way to test this in terms of moving items from one panel to the next?

Possible approaches:
1) Move available items over to the selected items list (16 at a time) and assert they 16 got moved correctly ?
2) Move items over one by one asserting as I go they moved ok
3) Save all available items to a list then add them all over and compared the selected items to the saved list.

Could threading be an option?

Arquillian, Drone and Graphene are used so tests are done with page objects using Java