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I don't understand this. Are you talking about the plastic bases described by the OP as being glued to bottom of the Naniwa, or are you talking about the type of box that some come in that double as...

Yes, it's okay to soak it with the plastic base. You don't want to soak it for a long time, but I have found that soaking for a few minutes works much better than spraying the top, which yielded...

Chamfer the edges, soak it for a few minutes, and hone away.