I hope that you get a reply from the Duke of Beaufort. There is a view that he will not go public unless he has already been tested in private and found something to make it worth his while to go public. In his case, it is difficult to see what that might be. However, we will see.
In this context, it can be noted that it is not impossible to get a noble/royal to take up the challenge of being DNA tested. As early as 1981, the mt-DNA sequence of the Duke of Edinburgh was determined. This is described more fully in Bryan Sykes, The Seven Daughters of Eve (2001), pps. 67-8, 71. The main results are summarised briefly at..
Note that when it comes to testing remains (such as of the Romanovs) the testing is on mt-DNA. The above web page describes various "famous DNA"; but, in all cases, the Y-DNA results are deduced from living descendants, not old remains. It is Y-DNA results that we require if we are to establish a DNA signature for the "Plantagenets".