I think the main issue, isn't necessarily that there is an MS which *states* it, but as you yourself pointed out in another thread, these MS can be creations to aggrandize their owners, *even* in the early modern period. They don't have to be 19th fabrications. Genealogists were fabricating in the 17th century as well.
The article by Rye which focuses on disproving the Steward royal claims, doesn't say much too much about the real line to Nicholas of the Temple, except that such a person existed. And other than the blank claims of the wifes from the MS, the author doesn't purport to support those at all. Just states them.
So we are still in need of a credible source for the name of the wife of William Steward buried at Ely Cathedral in 1593