I wish to state in all my lack of experience that regarding fingerings,
It's all good™
Several people have stated that on their instrument, the open C# isn't what the other notes around it are. It sounds thin and flat on both my Yams, but maybe of the hundreds of other horns out there, some of them have solved this problem. In looking at altissimo fingerings, I have found that what works for some simply doesn't work at all for me. I would assume that the alt C# mentioned work in varying degrees for different people/instruments. For me, Octave+R123 works great when I need a clear C# and for trills and tremolos, which in the blues are unavoidable.