I’m still a little confused. Has the wording of this document regarding the status and name of Kenya been debunked? or still a tossup?
I'd say it's a toss-up.
Kenya ceased being a Dominion on December 12, 1963, when they gained independence from Great Britain. But they didn't officially become a Republic until December 12, 1964.
In between, Jomo Kenyatta was named PM at the time of independence and was formally elected to the office in May, 1964 -- when the populace also chose to become a Republic.
Kenyatta was then installed as President and the Republic formally declared on December 12, 1964.
I suspect that, after December 12, 1963, Kenyan officialdom scrapped every form that identified the country as dependent on Great Britain. Then, it's conceivable that, for the intervening year, they chose to re-label the official documents "Republic of Kenya" -- even though it wasn't yet technically so.
After all, "Kenya, a third world work in progress" wouldn't have done...
Some are saying that Kenya did not become a Republic until 1964, while others are saying they were using “The Republic of Kenya” (in 1963) even before there was an official recognition from Britain (which happened in 1964.