Why would Richard falsify date of Hastings death from June 20 to Ju

I have been scanning my articles on the date of Hastings' death, and
one thing I am finding is that everyone from Hanson to the author
with good and seemingly airtight evidence that Hastings died on the
13th speculate about possible falsification of the records by Richard
III and his people, such that Hastings actually died on June 20 after
some semblance however slight of a trial, and Richard and his people
lied that Hastings had been summarily executed by Richard on June 13
in a fit of rage.

I am wondering what is the advantage to Richard of telling such a
lie? Why would he want to make it appear that Hastings was executed
on the 13th if he really died on the 20th?

I have seen arguments about Hastings' death relative to the removal
of the young Duke of York from Westminster, and I have seen the
argument that a certain relation between the two events would "prove"
that Richard plotted to take the throne having intended from the
beginning to do so, literally argued in both directions. The fact
that this argument can be made in both directions seriously undercuts
its logic.

I actually think the death of Hastings has little bearing on the
possibility that Richard plotted to take the throne. It was a stupid
move, if it had been plotted. I am fairly sure it was an attack
of "Angevin temper", the outbursts of extremely violent rage to which
all of the Angevin kings were inclined. Some of them were known to
actually roll on the floor and chew at the straw. One of them had
his lifelong best friend taken out and executed because he imagined
at dinner he had insulted him, and Louis the Pious of France, who was
sainted partly because of his largely successful struggles with his
serious mood disorder, once killed a servant by hitting him with his
bare hand because he had lost his temper. It is very consistent with
the massive signs that Richard and other members of his family had a
mild form of bipolar disorder or something much like it.

I think that Richard ordered the summary execution of Hastings in a
fit of violent rage and soon and ever after regretted it.

But if it is the story that Hastings was executed on the 20th, after
something that bore some semblance of a trial, why would Richard want
it to appear that he had effectively murdered him on the 13th?

Yours,
Dora