Honestly, I went to create a request: "Let us bind the furniture items". Because I struggled with inventory after opening the NM faction crates.
Suddenly, I found that my problem is solvable. However, you won't like it.

This is a part of my inventory.
You can see doubled items like Factotum body and Khajiit jug. They won't stack because some parts are bound and others are not.
You can see merged items on the top: Incense burner and Gravy boat. They were in two stacks the same way, but I put both stacks in the vault and then took them out. Now they are stacked.
It turns your items bound or unbound depending on the order you take them out from the vault. Once you do it, you can't turn it back until you find another item of the same kind.
So be careful, don't bind your items accidentally.
@ZOS_Kevin please could this problem be addressed?
I also hope we will have a feature "bind item" for furniture, so we could stack them intentionally.