There are 10.000 leaves stuck in infinitely looping itemduct network. How do I get them out?

Attach a void pipe or void chest to the network, eventually they will be purged, if your fast enough you can also attach a diamond pipe to filter them into the void pipe\chest.

If attaching an inventory to the pipes is failing, but breaking the pipes 'works' despite the lag, then create a method to handle the items after they fall out... a hole to the void, a hungry chest, a hopper to a void pipe, etc.