Did that still matter? Once he had been anointed and crowned, that had made him king, regardless of who ought to have been.
It would have been a simple matter to amend Titulus Regius to legitimise EoY and her sisters, while inserting a rider that "nothing contained herein shall impugn or affect the right and title of his Grace King Rycharde ye Third, now most mercifully reigning, and the heirs of his body - - -" . He could have his cake and eat it if he so decided.
But if he legitimizes EoY and her sisters, isn't he legitimizing the Princes in the Tower and at the very least asking for problems with Pretenders (of EV and Richard Duke of York)? Even if EoY is married off to a foreign power, what if Henry Tudor manages to marry the next York sister (Cecily of York), if Tudor still wins he could unite the two sides in another way.
Honestly, I think people will realize that Richard didn't believe his own reasoning for bastardizing EV's children And this will further undermine Richard's right to rule.
Iirc, in the legal opinion of the day, a foreigner could not inherit the throne. However, if the Lancastrians ran out of credible English pretenders, they might overlook this point.
Your absolutely right.