The main problem is that the author of theses backpacks (sengir) from the Forestry mod, will never ever fix it, he knows this problem is around since a lot of MC versions, and he refuse to cooperate with the guy that created Inv Tweaks to correct that issue, that's also the same reason why you can't shift click or use any of the Inv Tweak tricks when the backpacks are open. At least a trick that work, is make sure to keep at least 1 item in each backpack you own, and try to keep them in the green arrow or yellow arrow mode, this should fix the issue for now (it worked in 1.5.2 at least)