Ok, so I spoke to lots of places today about all this, and Kayell in Sydney said that there's basically no point trying to rewire the US version unit
because it's just built that way and wouldn't have the capacity to be changed. (?) Not sure what I think about that. They agreed that a transformer
would work, but then directed me to somewhere like Tandy or Dick Smith's (which are commercial retail places for things more like Playstation
and household electronics). So I got the feeling they weren't particularly expert in their represented brand of Elinchrom :/

Then I spoke to some electric equipment wholesale guys, all agreed that there should be no problem using the 1500W transformer to
power the units but that few places where I live stock that size one and I'd be best off looking on the net or interstate in Aus to buy one.
But I am still hung up on the finer details of making sure I don't kill the flash head, so now I have looked at a few websites who
specialise in stepdowns and all kinds of transformers, and they keep coming up with this list of questions (cut and pasted from one site here):

1. What is the total watts used by appliances to be connected to the Transformer?

Select from our Stepdowns range below based on how many watts your device uses*.

E.g: Playstation 3 uses 380 Watts so you need 500 watt stepdown transformer.

2. Does your appliance have a motor ?

If a motor is included then you should select a stepdown rating at least 25% higher than your motor as a buffer. Motors have higher power use on the stepdowns and startup currents which need to be allowed for. Most motors have a rating plate on them with their Power and Amperage rating.

3. Does your appliance have a mechanical timing device? If so, how critical is this timing device?

If a timing device is included the speed of the device may change due to the frequency change, 60Hz to 50Hz (eg old clocks, motors / fans)
4. Do you know the Amps of your device? - is so you can calculate the watts required:

Calculated as Watts = Amps x 110 Volts (eg 5 A x 110 V = 500 watts)
5. Do you wish to use multiple appliances from one stepdown?

Check total watts of all devices this must be less than the VA rating of the stepdown & get a US Powerboard

So does my type of flash head have a motor/timing device/heating element/pump/compressor ? I'll need to know this
if I'm talking to anyone I'm purchasing from, so I can get the right one. I'm just not sure if what's inside the guts of the
Style rx 600 could technically be called a motor, or if it would have any extra wattage needs that we haven't already
thought of?

Snederhiser, you're right, it would be a palaver trying to get new lamps/cords/electrician costs out the way before I could
use the flash, and it just seems like the transformer can do all of that in less steps.