Thanks. Is that the same issue on my 120/240 volt autotransformer type ballast. The ballast has two leads for a capacitor, but does not specify what value is needed. I measured a power factor of .6 and about 140 VA, same as my European choke type ballast setup.
Power factor 0.6 and 140VA means the capacitor has to provide 140*sqrt(1-0.6^2)=112VAr of reactive power. With the multitap ballast it is most efficient to use the highest voltage tap for the capacitor where the capacitors are still available, so the 240V one in your case. That means about 5.1uF (or 5uF if that would be more readily available), rated for at least 270VAC/60Hz of permanent loading.
But with the 120/277V transformer and PFC capacitor be aware, when the lamp would not strike, the transformer becomes again heavily overloaded, this time by the capacitor current. So better use some thermal cut out contact to protect the transformer...