I tried rotating the group labels in tha var chart that your attached file produced. It worked fine. Both manually and by the jsl code below. I am using JMP 9.03 for Mac. I include a picture so you can tell if I have understood the problem correctly.
vc = Variability Chart(
Y( :Y data ),
X( :X Group 1, :X Group 2 ),
Analysis Type( Name( "Choose best analysis (EMS REML Bayesian)" ) ),
Process Variation( 0 ),
Std Dev Chart( 0 )
);
Report( vc )[nomaxisbox( 1 )] << rotated tick labels( 1 );