I think z-value has nothing to do with clipping, it's just an order in which items are drawn on the screen.

Also I'm not sure what you're trying to do.
You're talking about clipping but you hide items with lower z-value.

Do you want part of the labels 'below' to be visible when obscured by other label?
Or do you want to hide labels that are even partially obscured by other labels?

To be able to help you, you need to share little more of your requirements.
Is the labels position static or dynamic?
Is the labels geometry static or dynamic (changing label content changes label geometry)?
What should happen if two labels of the same z-order overlap?

I would also question why all labels (thousands?) have the same parent item?
Can't you break them into smaller groups and investigate which one should be visible when one item in the group changes.
Also, because when zooming or panning, items themself do not change their geometry, none of the calculations you did to figure out what to show should be done again.