I'm not experienced enough to be giving much advice, but when I started taking lessons on alto several years back after playing tenor early in life, my teacher had me learn a much lower left hand position (farther down the tube) than I was trying and it made the left hand pinky keys much more accessible. Basically, I relearned to play with my left hand pinky playing almost parallel to the G# key instead of reaching it from from above. If your pinky is already at the G#, then the C#,B and Bb aren't so far away. Of course this changes the approach to the palm keys to a slight turn of the wrist instead of a slide/shift of the index/middle fingers. Maybe someone more experienced can comment on this idea or correct me. But I just thought I'd share that because it really helped me.