Yes, 1kW is more than enough. In fact, something like 3.5A briefly is more realistic for a startup current. Note you can cut required transformer VA rating to a much saner level by adding a PFC capacitor across the load!

Thanks.

In the case with my 200V 60Hz 250W mercury vapor reactor ballast where the line current during full brightness operation as 2.1A, I can safely assume that I would need a 1000VA transformer when factoring in a startup current of 4.2A where I get a startup VA rating of 840VA?

Mainly because their efficacy was terribly low and the life extremely short.

There was a fairly wide range of Argon glow lamps (AR-1 up to AR-9, a miniature type which was the UV version of the NE-2).  But due to the poor performance they were really only used in applications where UV output was required - which tends not to be in indicator lamps.

NB we also cannot really even talk of these being argon lamps, because all were in fact argon-nitrogen discharges.  Pure argon (or argon with a tiny percentage of neon, krypton or tritium to aid ignition) have even shorter lives due to excessive gas adsorption on the nickel, or nickel plated steel electrodes, or sputtering.  Despite intensive efforts, improved electrodes were never achieved.  Alloys or plated electrodes with lower gas adsorption suffered excessive degradation by blackening.

The solution to achieve coloured lamps was to switch to a neon-xenon filling combined with green, blue or yellow phosphors.  I believe Philips was first to make those at its Terneuzen plant in Holland, but Osram may have been first with at least the yellow (which it also offered with lacquer coating to produce green).  GE also extensively made the NE-2 Blue and Green models from the 1960s-80s.  These offered the benefits of long life like the traditional neon lamps, combined with much higher efficacy than argon-nitrogen lamps due to the phosphor stimulation method.

These days its not so easy to find the original Philips, Osram, GE or Sylvania neon glow lamps because those producers all gave up in the 1980s with the advent of superior LED technologies.  But the Soviets kept the designs running until much more recently.  You can quite easily find their ТЛЖ, ТЛО ,ТЛЭ, ТЛГ series for sale today.  I quite like those little lamps which were made in an unusually wide range if colours and illustrate the technology rather well.  I am not sure of their precise gasfillings, but suspect neon-argon + tritium and maybe also with a drop of mercury, at least in the -2 versions which have much higher voltage drop and hence power and brightness.

Yes.

The only argon glow lamp I know of is the AR-1 lamp, which was really only used as a small UV/blacklight source with a high purity glass envelope, never as an indicator. If you can indeed strike a discharge in argon with 120V, why was this never incorporated into small scale neon bulb style indicators?

Also, if you added mercury to a normal neon/argon penning mix indicator lamp, wouldn't that make it brighter/more efficient (and blue)? Why was this never done?

Because it will be dim. Low pressure Ar discharge emits significant part of its radiation in near-IR, useless for indicator application. UV generating efficiency is also mediocre, so practical phosphor indicator lamps usually have something added, like mercury or xenon. Adding mercury to phosphorless Ar lamp will make it somewhat brighter but not as bright as wanted for an indicator lamp, cause most energy of low pressure Hg discharge is radiated in UVC. Think of what you see in a germicidal lamp. Clear Ar + Hg  are often practiced in sign tubes, BUT you not always need a sign tube to be blindingly bright, instead often the opposite!

See here:

https://www.lighting-gallery.net/gallery/displayimage.php?album=8815&pos=0&pid=260418 Sag glass

https://www.lighting-gallery.net/gallery/displayimage.php?album=8815&pos=35&pid=255280 Flat glass

@NeXe Lights Do you have a photo of a 114?

If I have a reactor ballast where I do not know the startup current, should it be safe to estimate the startup current by multiplying the ballast’s line current by a factor of 2?

I've got a Ripley LongLife cell that rattles, it a small part of the board inside broke off, nothing important, just a little annoying! If I hold the cell above my head and look through the window and give it a bit of a shake, the broken piece falls down onto the window.

If it really bothers you, you could possibly attempt to remove the top of the cell, though that may just stuff up the whole thing. Not something that I've ever tried.