My suggestion goes as this:

Allow the Void Tear to store items and keep one stack of items at a time in an inventory
i.e. Tear absorbs all of the same item in an inventory without placing in the player inventory along with the items.
Examples: CC: Tweaked turtles could have a more space in their inventory so it isn't always filled with cobblestone.
Create schematic cannon will always have a stack of blocks available for it to use as to avoid filling up an adjacent chest.

Allow mode changing to occur in an inventories GUI (player inventory as well)
i.e. As the item cannot stack, right click the item should be able to change the mode.
Examples: Functional Storage puller and pusher upgrades allow you to right click on them in an inventory to change which side of the block they push or pull to.

If the first suggestion is added, another method to change the mode would be necessary as to avoid having to pull the void tear out of an inventory to change the mode then place it back into the inventory.

I'm not a minecraft modder so I'm not sure if the first suggestion is even possible, the second one should be as other mods have pulled it off but I'm unsure if that's because their item doesn't have an inventory.

Thank you!