When I open a chest, having just installed Zyin's, an item from my inventory is swapped with an item in the chest, seemingly at random. (This is with the ‘quick deposit’ completely disabled.)

This occurs randomly with Torch Aid due to restrictions of being a client side mod. One of Minecraft's function calls seems to randomly fail which causes my item swap to not work correctly when you right click on a right-clickable block, you have torches in your inventory, and have Torch Aid enabled.

I have looked into this before but without finding another way to implement Torch Aid (which was overhauled in v.1.3.7) I don't know how to fix it. Other inventory mods such as Inventory Tweaks also suffer from this issue.

Hm. So I'll have to disable torch-aid when using chests?

You could either disable Torch Aid and then re enable it when you need it (like when you're caving) or you could keep a torch on your hotbar which will eliminate the need to move items around, thus preventing the issue from occurring in the first place.

I personally keep it disabled unless I go caving.

Ah, so this bug only occurs if torch-aid needs to pull the item out of your inventory; not if it's also on your hotbar? That's good to know; I can easily dedicate a hotbar slot, but I really do like the torch-aid mechanic.

This might be something worth putting in the ‘known bugs’ on the forum thread, or even on the options screen. Perhaps even disable pulling torches from inventory, and document the feature as needing your torches in the hotbar, until it can be fixed upstream? That's a pretty terrible bug!