I thought the only things that couldn't go in either the dresser or armoire were pieces with unique extra information that those features can't reproduce when the item is removed, like relic weapons with customizable stats, or a wedding ring that has an extra field to identify whom you're married to. But I don't believe there are any such extra fields on an Onion Doublet, so it should be allowed.
It's possible that between when the dresser was introduced in 4.2 and when it was updated to allow removal of items in 4.3, there may have been additional restrictions to block really rare items from being placed there, since for that original version you couldn't get things back once put in the dresser. (I don't know if that's the case, but it would kind of make sense.) If so, that could account for why it didn't work before. It's worth trying again to check whether it can be placed in the dresser now.