We currently can't use Inventory Tweaks in the backpacks' inventory so I've configured some compatibility informations in the file config/InvTweaksCompatibility.xml:

<root>
   <chest class="net.mcft.copy.backpacks.container.ContainerBackpack" row_size="4" large_chest="false"/>
</root>

And it works!
But it would be better if you could use the Inventory Tweaks API for an out the box compatibility.

Inventory Tweaks always comes back to haunt me, whether it is as a player or as a mod developer.

Thanks for providing information on how to add compatibility as player / modpack author. I'll see if I can get this added some time. Welcoming PRs for this as well!