You seem to have no understanding of history at all, certainly don't understand Richard III or Henry VII at all.
First lets deal with Richard III, he was a highly religious man who spoke out against immorality and adultery. We have documented evidence for this. Their was no relationship between him and Elizabeth of York at all. In fact Richard probably saw very little of her throughout her life.
Elizabeth could never have become Richard's Queen without negating his own justification for the grabbing the crown of England. Elizabeth had been declared by parliament to be a bastard, a King could not marry a bastard. It was that simple.
Then we have the fact that The Portuguese marriages were well underway prior to Queen Anne's death.
Elizabeth was considered mainly because she was the eldest, I have speculated that if Richard's own bastard daughter Katherine (Born before his marriage) had not been married in 1484, she probably would have been used in the alliance not Elizabeth. Marriages between bastards and Royal Dukes, while a bit uncommon, were not prohibited by canon law.
Second we have the fact that Elizabeth would have brought nothing to Richard at all. The majority of Yorkists supported him, the tensions between him and the Woodvilles had cooled down considerable, Elizabeth had no dowry to speak of, she would have brought nothing. Joanna of Portugal on the other had not only brought a dowry, but she brought Lancastrian blood, she was a direct descendant of John of Gaunt through the legitimate line. That blood connection would be highly important to any children he and Joanna might have.
And now lets go back to your idea that just because Edward IV made a foolish marriage means his brother would. Edward IV marriage literally shocked all of Europe. Richard has no indication at all that he would not do his duty and marry for his rank and station. He originally married Anne Neville because of this, I don't doubt that Richard would later marry Joanna for the sake of his country.
And now the idea that Richard didn't visit Anne on her death bed. We have very little on the contemporary record, but what we do know is that Richard had to state the reason why he was no longer sleeping with his wife. This does not mean he did not visit her, just that Anne was thought to be contiguous and that Richard's doctors feared he would fall ill if he slept with her.
And this also indicates that Richard up until this point had been actively staying in Anne's bed. That is was well known at court that Richard and Anne slept together. Given how unusual it is for royal couples to consistently share a bed this indicates closeness.
And lets go to the Buck letter, it either A. didn't exist, It's highly probably that George Buck was trying to one up his other discovers. Or B. was misinterpreted, we don't have the full letter, only scraps which Buck remembered. Since the information about the Portuguese marriages did not come out until the 1980s, it highly possible that the letter was about this. That Elizabeth was asking about her being married to Portugal. Since their was another offer Richard recicived from Spain which did not offer Elizabeth a bride-groom. It was very possible that, being 18 years old with an already married sister, wanted to be married.
Second who is the letter addressed to, John Howard the Duke of Norfolk, one the most loyal men to both Richard III and Edward IV. Do you honestly believe Howard would have supported Richard if he felt he was dishonoring the daughter of a man he loyal to.
If anything the fact that Elizabeth had to write to Howard indicates she was not close with the King, and needed someone to intervene on her behalf.
Now lets go to the idea that Henry VII waited to marry her to see if she was pregnant. One this couldn't have ever possibly been the case, Richard had been in the same as Elizabeth of York since March of 1485. Second their were three reasons why the marriage was put off until January, one so that Henry could establish his own rule, he could not be seen as a man ruling through his wife, especially if Elizabeth die before him, or had no children. Second he had to have parliament confirm legitimacy on the children of Elizabeth Woodville and restore them to their station. And finally is that Henry had to wait for a papal dispensation for them to be wed, he had one in 1484, for an Elizabeth Plantagenet and a Henry of Richmond, but wanted to ensure the marriage would never be called into question so he wanted to have one granted for Princess Elizabeth of York and Henry VII of England, a specialized one came in January of 1486, which is when they wed, and the formal one came in March of 1486. This was to ensure the Tudor Dynasty's legitimacy.
All of this took an incredible amount of time, planning a coronation, setting up a parliament, and then getting a papal dispensation. Remember were talking about the medieval where traveling could take weeks.
So no your idea is ludicrous and isn't supported by the facts of the situation. I suggest you go back to fiction because that's the only world in which Richard III would ever think about marrying his niece.