@jmcferren:

Calculating the ballast in that way (the impedance only) does not work. Beside the correct current, the ballast have to provide sufficient voltage for the arc restrike after each current zero cross. For a series choke ballast this impose a limitation to the arc voltage to not exceed about half of the mains voltage. With a series choke you have only the mains peak voltage for the lamp to reignite.

And you should not forget, than the voltage across the tube is nearly rectangular, so the simple "vector math" does not work anymore, when the arc voltage become close to the mains.

On top of that the ballast should maintain the current even over some mains voltage, as well as real lamp arc voltage variation, with so little voltage margin and no stabilizing element the spread would be simply too large.

What help (although I'm not sure, if the nearly 100V lamp is not too much even for that) is the use of a series LC, operated off-tune on the capacitive side: For first harmonics the capacitor's and inductor's impedances subtract from each other, forming the desired 44Ohm. But what makes it way different from the simple series choke and what is very important with discharges are two aspects:

First, when the current crosses zero, the capacitor is charged to it's peak voltage (corresponding to the designed impedances) and when the arc extinguish during the current zero cross, so the current stop flowing, the capacitor voltage add up to the mains, so the lamp have way higher voltage available for reignition (practically you can reach at least double the mains peak voltage).

Second aspect is related to the fact, than typical ballast coil lower their inductance at higher currents (part of the core saturate). Now if such coil is part of an series LC ballast operated on it's capacitive side, this reduction of the inductance at higher currents cause the LC to detune even further, so increase it's impedance. And higher impedance mean lower current, so the core saturation in fact mean the current stay pretty constant over quite wide voltage range, a feature you need when the lamp voltage approaches the mains, just to compensate for variations

But the manual start or a special electronic starter is still necessary, as all the effects before start to play their role only AFTER the current start to flow.

By the way this method is used in commercial ballasts, e.g. in

this ballast , but only till F30T8...