Thought I'd give an update and tips on my endeavours on replacing my rear brake lights and rear indicator lights with LEDs.
For the rear indicators, I ended up having no other solution but to install load resistors in parallel to the LED bulbs to avoid hyperflashing. I mounted them to the aluminium chassis behind the rear light assembly with heat-resistant tape (quite poorly, I might add; the surface wasn't flat and would function mediocrely as a heatsink). I'm fairly confident they're not touching any wiring and it won't melt through anything, though.
Through my testing, it's also worth noting that the front and rear indicator circuits appear to be independent, i.e. installing two load resistors for each globe at the rear (four in total at the rear to dissipate the equivalent of four halogen globes) will *not* let you install LED indicator bulbs at the front. The reason I contemplated this was because the wiring for the front headlight assembly is wired through a giant plug with all the wiring bundled together. Though it's possible, I wasn't confident enough to find the correct wire and mount a resistor somewhere neatly at the front.
For the rear brake lights, I bought some (fake Chinese) Cree LED globes similar to my indicators. I advise not to go too cheap when buying these LEDs as some of them are quite poor in distinguishing the brightness difference between the bright 'brake' light and the dimmer 'tail' light when your headlights are on. This is quite dangerous at night and will undoubtedly violate some ADR standards. Luckily, mine were comparable in performance to the stock globes. I would also expect the really cheap LEDs (or perhaps even all the ones off eBay), are poorer binned LEDs. (By binning I refer to the categorisation of high and low performing LED chips due to the imperfect processes of semiconductor manufacturing.) Also, for the record, I did not have problems with cruise control after replacing my brake lights with LEDs.
Now, the brake lights are 'dual filament', where in a halogen globe there are two actual physical filaments for the bright 'brake' light and dimmer 'tail' light. This means they are completely isolated. The LEDs I bought is one circuit and had very poor isolation between the 'brake' circuitry and the 'tail light' circuitry. When the LED tail lights were on, their voltage leaked to the brake lights. This meant that my middle brake light was being fed voltage and was lit dimly when my tail lights were on at night (they were fine in the day, because the tail lights are only on when the headlights are) (also, the middle brake light still lit brightly from the dim state when the brakes were applied).
I solved this problem by soldering a 1N5404 3A diode from Jaycar to the brake light wire so that voltage cannot be fed backward to the middle brake light. The 3A rating means the diode will still operate under spec even with normal halogen bulbs. Now, there are three wires (red, green and black) going to the brake light globe holder, you wish to cut the green one to solder the diode in. You'd naturally think the red one would be for the brake light, but it's not. I can assure you through my trial and error. (I ended up having to install diodes on both sets of wires; unsoldering the other would've been too messy). After you cut the green wire, strip the two ends and solder the diode in between. You'll also want to heatshrink or electrical tape your solder joints after you're finished.
If you encounter my same symptom of a dimly lit middle brake light after changing to LEDs, I'd retrospectively recommend you use a Schottky diode (a 1N5822 will do) instead of the one I used, as they have half the voltage drop of a regular diode, meaning your brake lights will be brighter. I note however that I couldn't tell the difference in brake light brightness between having the diode present (11V being fed to the lights) and it being not present (12V being fed to the lights).
Overall, I'm quite happy with this little project. The brightness of the LEDs I chose are more or less the same brightness as the stock halogen globes, but now my rear lights turn instantly on and off. I'm a bit bummed I don't know how to replace the front indicators with LEDs, but I've already bought more LED globes to replace my 2nd rear tail light, reversing light, licence plate light and front parking lights. I might give another update when they arrive in a month from China. I don't expect that many problems as that LED brake light, however.