There are a number of weak points in your argumentation.
1) That Chief Tenaya used a Paiute Jargon (and not just Paiute) has no bearing on the original Ahwahneechee dialect. It was presumably because after his return to Yosemite there was a mixed population present, among whom a large number of Paiutes, who had accompanied him back there.
2) The word "Ahwahneechee" meaning 'people of Ahwahnee' is a type of formation met with in the Miwok (and Yokuts) languages. The word "Monache" is also funnily enough a nice example, being the Yokuts word for 'Mono'. "Pohonichi" is another one close-by, referring to the Miwok who derived their name from "Pohono".
The Potoyancies and Awalances were certainly Miwok. But not of any relevance for Yosemite.
3) Why Jay Johnson would or should have any special knowledge of the language spoken in Yosemite in Tenaya's childhood is unclear to me.
4) "Ten-ie-ya replied, as the young Indian stepped forward by his direction, "I will go with my people; my young man shall go with you to my village. You will not find any people there. I do not know where they are. My tribe is small--not large, as the white chief has said. The Pai-utes and Mono's are all gone. ..." (Burnett)
This doesn't sound as if he reckoned the he Pai-utes and Mono's as real members of his tribe."
5) Unlike the Paiutes, the people anthropologists and ethnographers call Miwok did not use the term "Miwok" to refer to their tribelets. The word Miwok just meant 'person'. The Southern Sierra Miwoks alone had about three dozen rancherias. The word Yosemite is, as you kanow, derived from the Southern Sierra Miwok for 'bear'. So "Yosemites, Monos and PAIUTES" would not be an unexpected way of referring to the different groups. Once again, it certainly doesn't suggest that "yosemites" including "Paiutes".
6) "I afterwards learned the traditional history of Ten-ie-ya's ancestors. His statement was to the effect, that the Ah-wah-ne-chees had many years ago been a large tribe, and lived in territory now claimed by him and his people. That by wars, and a fatal black-sickness (probably small-pox or measles), nearly all had been destroyed. The survivors of the band fled from the valley and joined other tribes. For years afterward, the country was uninhabited; but few of the extinct tribe ever visited it, and from a superstitious fear, it was avoided. Some of his ancestors had gone to the Mono tribe and been adopted by them. His father had taken a wife from that tribe. His mother was a Mono woman, and he had lived with her people while young. Eventually, Ten-ie-ya, with some of his father's tribe had visited the valley, and claimed it as their birth-right. He thus became the founder of the new tribe or band, which has since been called the "Yosemite."
By this account there's no necessity for the Ahwahneechees to have had any connection with Paiutes before their doption by them. In any case, as I said above, "Ahwahneechee" is a Miwok word.