No you cannot just rewire a three phase motor so it will run on a single phase supply,
you can how ever get a electronic convertor / motor speed control
not cheap mind you but will work splendidly
pin holes and leaks in heating elements is very common,
one or more of your elements is leaking to ground.
once you have worked out which one ( by a process of elemination )
then replace it with a new one.
You sure do in Australia, anything that plugs into the mains, you need a minimum restricted electrical licence, you need to be registerd, and carry 2M insurrance.
the X-10 would likely use a semi conductor to switch on your light,
(this is the problem) it is not compatible with the electronics in the flame bulb.
so use the x -10 to control a relay and use this relay to switch on the flame bulb.
IT'S POSSIBLE !
But remember that most space heaters use plenty of electricity, so you will need plenty of panels and some batteries if you want to go into the evening, all possible but not cheap.
Try this out -
https://www.amazon.com.au/Yescom-Precision-Variable-Digital-Adjustable/dp/B075LK6CW9/ref=sr_1_2?keywords=adjustable+power+supply&qid=1574055336&sr=8-2
since the LED lights only need 3.7v, then a 12v transformer is not best suited.
A lower voltage like 6 or 5 v would be better,
Then use a resistor to trim the voltage
Or perhaps wire 3 lights in series.
you can use a 240 > 120 backwards
to boost 120 up to 240
such transformers are readily availible
https://www.ebay.com.au/itm/110-120V-to-220-240V-Step-Down-Up-Voltage-Converter-Travel-Adapter-Transformer/153429250799?hash=item23b91892ef:m:mclWlPx9Rf4IcrJlBkh-uhw
if your happy that sheilding the wiring is the answer ?
Then just put all your house wiring in metal conduits,
if all the wiring is in metal coduits and metal j boxs and all this is
properly grounded,then your covered.
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