Would the mouthpiece-to-keys distance be about the same for the Shakulute and transverse headjoint?
Not quite. In constructing the shakuhachi headjoint to produce the same pitch as the transverse flute, the distance from the utaguchi (shakuhachi blowing edge) to the keys is just a bit longer than the blow hole of your transverse headjoint. This distance, however is very slight (less than 3/4″), has no effect at all on fingering and is the same for instruments with either a C or B footjoint.