On the 18W choke it it stated 18W 220mA, measures 107 ohm coil resistance
It would overload the lamps. The PL-S9W are rated at 170mA, so the 18% (200 vs 170mA) overload is too much (getting even worse during preheat).
Just any "7..11W PL-S" ballast works fine (the arc current will be in the 0.14A range, but more important for the life is the preheat current and that remains the same as with only one lamp - filaments are nearly a short circuit with respect to the ballast impedance)...