If we assume the HD Wii would lose all of its casual titles, then we have to assume it would get some major HD games. Perhaps it would get a Zelda Breath of the Wild, or a Splatoon. The Wii got a lot of quality games in its first years, so the HD Wii would have gotten even more. Consoles sell due to games, but the HD Wii would have lost the blue ocean crowd. So I will call it a narrow loss, but still satisfactory performance. Overall 7th gen sales would be much lower, and the PS2 would have gained a bit by being the cheap popular casual console. Due to the PS2 continuing to do well and the PS3 being the most expensive out of 3 expensive consoles it would have lost even more. 360 would be the eventual winner with kinect and more momentum early without a cheap Wii.
So without further ado here is my estimates.
Wii HD- 67m
In my mind I am trying to do as minimum of a change as possible. All of the "Wii ____" games just disappear, like Wii Sports, Wii Fit, etc... as well as any game that relies highly on motion controls like Wario Ware and Fling Smash. These get replaced with nothing to reflect the higher development costs of HD. On the other hand a lot of other games that have motion controls just get conventional controls: Mario Kart, Wario Shake It, New Super Mario Bros Wii, etc.... Twilight Princess is their big launch title, and all of their games get HD graphics. Visually they would probably look a lot like the Wii U versions.
Given all of that, their first party has some heavy hitters that the Gamecube did not have. NSMBW has sold 30m+ copies and Mario Kart has sold more than that. Those games would still be popular if you took away motion controls. The Virtual Console also would be a big hit with old schoolers. Basically if you take out motion controls they lose the new motion control crowd, but they would still get a lot of old school gamers with both the VC and games like 2D Mario, Donkey Kong Country, Mario Kart, etc.... It would not be a Gamecube 2. And because it would have good sales, then it would get a lot of HD multiplat games. I stand by my assertion that the generation would be close to a 3 way tie.
I do like your sales assessment including that the PS2 would go up in sales. The lack of cheap console would help the PS2 even more (and maybe the DS too). I was thinking more like an extra 5-10m though.