Hi CJ, I haven't hiked that entire loop, but I've been into Cottonwood Lakes several times. You might consider staying a little lower the first night, maybe at Long Lake. Staying a little lower will help with the acclimation.
And your second day with almost 12 miles, half of that cross country looks ambitious. But then, you could camp anywhere along Rock Creek, so if you don't make Sky Blue Lake, it wouldn't be bad. Once over Crabtree pass, it should be an easy cruise to Guitar Lake.
By the fourth day, you would be pretty well acclimated, so the trip to the Whitney summit ought to be just fine.
RoguePhotonic's
photo from Langley toward Mt. Newcomb (upper left) shows Sky Blue Lake (lower left) and Lk 3697M (12129ft) (upper right) which is just south of Crabtree Pass. Crabtree Pass is on the right edge, behind the peak/ridge at the upper right edge.
Here's his picture:
It looks like a sweet adventure. Just make sure you and your your "rusty" companions don't pack too heavy, or the altitude and exhaustion will ruin the fun. Read the
Lightest weight hiking gear thread for ideas.