If you were to take the lockring off your cassette, you'd see tiny splines on the 11T cog which help keep the lockring from loosening. The problem with your idea is that the other cogs on the cassette don't have those splines, so there is a chance that the lockring could come loose more easily. Miche makes replacement 1st-position cogs, so if you got a 13T cog intended for that job, it should work.