To save you a lot of trouble you will not find those records and claims of, for example, George Washington was descended from William the Conqueror are falsified little white lies. The paper trail breach from the Conqueror to the 1500 century families doesn't exist. Not in George Washington's case or in your cases. After a royal family falls out of succession in cases where they were forced from power with progeny they become mundanely average and unnoticed in the annals of history and typically try to be as unremarkable as possible for their own safety from those foaming at the mouth with lust for power.
Given the historical importance of those families it is possible if remains are ever found that DNA is extracted and you can verify or dismiss your suspicions by taking your own DNA test.
For example, on the paternal side, I know for a fact there are 3 families related to a common male ancestor with the last name of Grogan (probably the same man, Thomas Grogan) we had in central colonial North Carolina around the time of the American Revolution via a DNA test. On the maternal side, I have found that of all the mtDNA tests given to date I match the mtDNA of two men. One is has documented Amerindian ancestry and myself and the other can only trace back to a women of European descent. However all three of us can trace back to different women of European mtDNA ancestry that managed to have children but never had a husband that anyone could document and all three of these women migrated from the same area of the Appalachian Mountains near the Smoky Mountains. There ancestry seems to be from an Amerindian male and a European women before 1800 in the area near the Smoky Mountains but their will likely never be a paper trail found so I will have to build a puzzle with missing pieces. That will be enough to say on this puzzle is of a, e.g. watermill, but will leave out interesting details had a written history existed.
So DNA can get you tantalizingly close to proving the truth of your ancestral origins if they should ever collect DNA from the remains of those two families you list and you compare your own results with those families. It's still not absolute proof of descent. For example, those 3 'unrelated' families to my Grogan family with last names different from Grogan that have Grogan Y DNA from colonial North Carolina... well the fathers contributing that Y DNA in each case may have been three different men with the Grogan last name. You can't even say how those potential three Grogan men were related without tracing back to a common male ancestor of theirs. In this case that ancestor would be Thomas David Grogan (Groghan/Croghan) of Kings County, Irland from the early 1700s.
My maternal grandfather was a Farley so he descends from families closely related to the Conqueror and thus often titled landowners but that doesn't make the families he descended from royalty or descended from royalty, it made them nobility.
That is a big difference and one most people don't get. Nobility is a pledge of allegiance to a crown or a royal family, not royalty itself. And although nobility through the centuries often ousted royalty through force much in the same way military officers oust political leadership in the modern world that they ousted by force flies in the face of the definition of inherited royalty. So those noble families that never ascended to royalty via force don't become royalty simply because other nobility did ascend to royal status via force.
And after the age of conquests, the requirements of nobility typically evolve into financial success and fame. e.g. I am not descended from nobility via my Grogan ancestors, however, eventually one family of Grogans was granted nobility by the crown but it was for that family and it's descendants only. And if any descendants to that family still exist they may have inherited properties but I doubt they are still technically considered titled nobility. Maybe a expert on that could clarify that matter. As far as I know in the current modern age, nobility is just a lifetime title that can't be inherited but it is granted by the crown for those that are famous and financially successful. Queen Elizabeth is given a long list of vetted people to grant such titles every so often.
Good luck.