It seems to go without saying that killing children is wrong but many of Richard’s predecessors killed off unwanted deposed kings. Did he simply think killing the Princes was an extension of this or were there other things in play? Or are there legitimate reasons to think he was framed?
I have disagreements with "backlash" and "many ... killed off ... deposed kings".
"Many of Richard’s predecessors killed off unwanted deposed kings" overstates the matter. Since the Conquest:
All of these, by the way, were not declared to have been "killed off" but simply to have died in captivity, though anyone who actually thought that Henry VI died a natural death was hopelessly naïve (details on request). Well, all but Arthur -- he simply disappeared.
Edward V: Too young to have become unpopular, and Mancini wrote that he had charm, dignity, and educational achievement. Son of a reasonably well-regarded late king. Deposed by his uncle, a close kinsman, his Protector, who had just sworn fealty to him. John had some trouble from Brittany about capturing his nephew Arthur.
About "backlash": how much contemporary backlash was there, and from whom? I don't know clearly, and I'd love to know more.
Lord Hastings, one of Richard's early victims, might have been executed for opposing Richard seizing the throne ... but Hastings had been devoted to Edward IV and was a natural leader for Edward IV's household. The rebels of 1483: southerners (Kent to Cornwall, south of Thames), loyal servants of Edward IV. Henry Tudor: inherited the Yorkists when men came to think that Edward V and his brother were dead. The French: backing Henry Tudor. Commynes: servant of the king of France.
If there was a backlash, it didn't seem to affect Richard's northern supporters in the least -- if there was a problem, you'd think that some might have left him then.