When I imported a SOX lantern from the UK without gear, I decided to try running 35w SOX lamps on a F40T12 preheat ballast using a European 35w SOX ignitor. When the lamp fired up, it had a very flickery startup and when I tried doing a hot restrike, the lamp produced a wild flicker and eventually stabilized with slight flickering. I understand that the lamp was underdriven by about 0.2a from its rated current. How long should the F40T12 ballast and 35w SOX lamp last?

SOX18 is rated for 0.36A, not 0.2A.
And the 0.43A ballast is overloading it due to two reasons:
First obviously the 0.43 is greater than the rated 0.36A.
Second the F40 ballast is designed for a 105V lamp, so operating a 57V one will cause the current to become even slightly higher. How much, depends on the exact ballast design (the level of shunt saturation), assuming about 15V resistive (= in phase with the current) drop in the ballast and about 220V OCV (what I would expect for a F40 preheat), it means about 12% further increase in current. In total it would mean 33% overload of the lamp, which would be quite a lot. LPS are not well suited for any power alteration, they are thermally on the edge just as they are designed: Any colder and there becomes too little Na vapor pressure for an efficient operation. A bit above and the arctube starts degrading quickly (Na is rather aggressive towards virtually any fundamental material in the lamp, so the components requires special coating to passivate them; and this uses to be quite fragile, the extra heat wont make it any stronger at all. And once that coating cracks, the Na will attack the glass base material very quickly and aggresively)

But question is, what is the real F40 current, as it was common for F40's to be operated at reduced power (either to attain lower intensity to home use, or allow efficient operation at higher temperatures).
So connect an A-meter in series with your lamp and you will see.

What effects will I see if I wire 2 18w SOX lamps in series on a F40T12 ballast where FS2 starters are connected in parallel across the lamp sockets?

What effects will I see if I wire 2 18w SOX lamps in series on a F40T12 ballast where FS2 starters are connected in parallel across the lamp sockets?

The circuit will see two pairs of cold electrodes in series, so the OCV may not be enough to build up enough current to warm them up and transition to arc.

You should not forget just gas breakdown is not enough to starts the lamp.
For tge first gas breakdown the short pulse from the starter or ignitor is good enough.
After breakdown, a cold electrode glow discharge starts. This discharge has way higher voltage drop than nominal (I would guess about 100V above normal operating voltage), so need higher ballast OCV. But it has to provide enough (ion bombardment) heat to warm up the electrodes, so you need a significant current flowing for a long enough time, so it has to be provided by something more energetic than just an ignitor pulse. Usually the bulk ballast OCV is doing this job.
And only when a significant current has been flowing in the glow mode for sufficient time, the electrodes reach thermionic emission and so tge lamp voltage drop decreases to its normal operating level dictated by the present pressure. Normally it takes about fraction of a second or a second in the glow disvharge state to warm up the electrodes, so the glow stage uses to be overlooked. Of course, if tge lamp has provision to warm up the electrodes before the ignition (fluorescents, arctubes in 120V SBMVs,...) this glow phase is skipped over entirely, so the setup does not need the extra OCV anymore.
Then (depends on the lamp chemistry) the lamp eventually warms up so the arc voltage reaches the rating figure.