Maybe an alert is not the best case here. Since alerts are more for short, immediate messages, not full scrolling lists like that. A modal would be a better option.
If I could display a popover in the middle of the screen that would solve my problem.
I think the best way to accomplish your design is indeed to use a popover component. In the template of your popover you could place any html you like.
Attention: due to a bug in the current beta 11 you must put the popover’s template inline to your popover page in order to have it displayed centered.