Thank you very much for sending your project. I was able to identify the problem.
The issue was that the equipment root node does not match the master root node.
I made the wrong assumption that the root node would always be the same, but doing more research I found that it isn't allways the case.
It was quite a troublesome bug to fix but your project really helped me test it out. So again thank you for the sending us your project.
Now the Equipper keeps reference of the master root node and all the character bones.
Then when a new skinned mesh equipment is added i scan all the character bones to see if I can find the matching ones by name.
I remove the equipment bone hierachy to cleanup the hiearchy since they aren't used and then link the equipment to the character bones.
Note that now the items are still pooled but they are pooled specific to a character, meaning different characters won't be able to share pooled items. That's to avoid bugs with linked bone hierarchies.
Specific to your game, you'll need to remake the Helmet and Chest Armor prefabs. The Helmet has issues with its bounds, and the chest armor is missing a material. Remaking them from scratch should be easier than trying to fix them.
Additionally you can remove the Rigidbody from the equipment.
Please find the new Equipper and ItemObjectSlot scripts attached.
I hope that with those changes you won't have any more problems with equipping items.