First you forget to couunt with the less than unity lamp power factor because of the voltage (nearly rectangular) vs current (nearly sinewave) shape mismatch sqrt(2)*2/Pi()=~0.9, but that does is, indeed, not the main problem there. You are correct with the sensitivity calculations: More you want to compensate by the capacitor, more it become sensitive to ANY tolerances in the L and/or C. If you make the circuit on the capacitive side, one effect would play a significant role in helping you: As the core get higher flux, more and more of it's parts saturate (first some edges, then touch points,...), so the inductance goes down as the current increase. So what happen in your circuit tuned for the capacitive side operation? Let's assume the circuit is exactly in resonance when there is small current: Xc=926Ohm, Xl=926Ohm, so the total Z=XcXl=0, so when the voltage is applied, the current start to build up, as the energyu is pumped into the resonator. But as the current build up, the inductance goes down, so does the inductive reactance. But as the total impedance is XcXl and the Xc stay the same, it mean the overal reactance start to rise, so eventually would limit the current in the circuit to an equilibrum, where the inductance is just reduced so, the impedance yield the corresponding current. If the circuit condition change so the current would rise with the same impedance, the increase of the current cause the inductance to drop further, so the overall reactance to increase, so reduce the current rise. You see, than this LC ballast then provide a kind of current stabilizing role  with changing external conditions (mains of lamp arc voltage) it changes it's impedance so the current change only little. The same mechanism then compensate the component tolerances: Higher current cause lower inductance, so compensate for anything, what changed the higher current and vice versa.
So for real design, I would calculate the circuit for the mean values of all parameters and let the stabilization effect take care of all the variations.
But for the current stabilizing effect have one adverse effect for fluorescents: The current remain pretty the same even during preheat by the starter, while the lamps are usually designed to be preheated by somewhat higher current, expecting the ballast slight saturation cause the current to increase. So the preheating would take longer, so the system would become more "blink happy" with ordinary starters.
And there is yet another effect from the series LC operated below it's resonance (so with dominant capacitance): Lets assume the lamp light. With this, the nominal current flow through the circuit. Now assume (for the sake of this explanation, for real circuit it does not matter) the circuit is arranged so, the capacitor is just between the phase and inductor, the lamp being between the inductor and Neutral. If you observe the voltage on the middle point between the capacitor and inductor, you would see something like 270VAC. So replacing the 120V mains with the capacitor by the 270V AC source should not change anything for the inductor and lamp, right?
Now what happen, when the current reaches zero cross: Lamp arc disappear, so the circuit become open (for the short instant just after the zero cross). That mean the voltage across the lamp would be the sum of the capacitor and mains voltage, so the peak of the 270V, so about 380V.
But wait a minute, we have 120V mains, but for lamp reignition we have 380V peak voltage available. Now there is flying around "The mains voltage should be twice the lamp arc in order to allow reliable zero cross reignition", isn't the 270V then the equivalent "mains" for the reignition? Well, it in fact is. And it is this effect, what allow to operate lamps with higher reignition spikes, so arc voltages. Well, as the arc voltage rise, the voltage available for reignition drop a bit, but still it remain quite high. Of course the lamp arc voltage should be still low enough, so the ballast could deliver the required current.
Taking into account the current stabilization ability, this arrangement allow to operate lamps with arc voltage up to ~80..85% of the mains voltage, so for 120V mains it would be up to 100V lamps. Well, F30T8, FC12T9,...  all these could be operated without the transformer. But what remain is the problem with starting: Before any current flow, there is just the mains voltage across the lamp, available to trigger the starter. Only after the starter close, the higher voltage build up. But that mean the starter trigger voltage have the room only between the lamp arc voltage (100V, with 200V reignition spikes should not trip the starter) and the mains (120V, so ~160V peak should reliably make the starter closed). So it is this reason, what keep the usable lamp arc voltage below 60..70% of the mains. In order to go really up to the 85% limit, the starting system should respond to something else than the voltage value across the lamp, so e.g. the tube light (manual start) or circuit current (4 pin thermal starter).
