Your question was about 'Capitalizing “The” in styles of nobility'. I answered by showing that in the press and on TV news sites, in the UK at least, it was normally uncapitalized. Those newspaper and TV companies publish style guides for their staff. The articles I directed you to were written by journalists complying consistently with those guides: using 'the', not 'The'.
The website you linked to, where "The Queen" is given a capital T, was no doubt written by some entitled - or even titled - young things, offspring of the gentry. Like members of the royal family these people are not expected to be very bright or highly literate.
You asked, "For works using this writing style, is there any standard guide to when the article is capitalized?" But what IS this writing style? You say it is unusual. You say it is one with real use. (I'm not sure what that bit means.) Would you characterize that style as 'inauthentic Olde Worlde English'? If so perhaps John Irving's 'Jitterbug Perfume':
"The Christians doth be everywhere.”
"If Pan be alloweth to die..."
would be useful.
Several of those style guides are accessible online. As I said, they show the correct use of capitals. Guides showing how to write badly are thin on the ground.