I found this extract on a website, and it supports my revised view that this garment was not worn until after the Anointing and a prayer -

This prayer being ended, the Queen shall arise and sit down again in King Edward's Chair, while the Knights of the Garter bear away the pall; whereupon the Queen arising, the Dean of Westminster, assisted by the Mistress of the Robes, shall put upon her Majesty the Colobium Sindonis and the Supertunica or Close Pall of cloth of gold, together with a Girdle of the same. Then shall the Queen again sit down; and after her, the people also.