There is also another problem with "reducing CWA power by changing the capacitor":
Normally these ballasts are designed with the inductive component in series with the capacitor to be current dependent (shunt saturates, so reduces the inductance when the current goes higher) and by that detune the series LC so the current stays where designed. This current is dictated by the point on which current the shunt saturates. This forms very strong current stabilization mechanism, which suppresses very broad mains voltage variation, as well as to big extent even the capacitor tolerance.
If you just reduce the capacitor, you decrease the lamp power, but the shunt won't be saturating anymore, so the current stabilization effect will be gone.
Does not have to be that much of an issue when the mains voltage and all components stay within tight tolerance or when it is used just to dim a higher power lamp where the tolerance for the exact operating power for that settings is very wide.