I also think she is Mary Tudor, maybe late teens or early twenties?
About the Jane Grey-Catherine Parr portrait, I still have my doubts... I mean, the face of the sitter doesn't look the same to me than that of the most famous portrait of Catherine Parr and, on the other hand, at least for me, I see a similarity between the sitter and the engraving of Jane Grey that must be somewhere. The fact that the lady uses jewels belonging to Catherine Parr could both mean that she was indeed Catherine Parr, but could also mean it was the Lady Jane, using jewels that Catherine could have given to her when she Jane lived with Catherine and Seymour...