Gidday Mate, always nice to have another Kiwi on the boards!
(Steve, I'm based in Whangaparaoa if you are looking on google earth Lat -36.582993° Long 174.664193°. Check out my new motorway!)
Given your cars age and the description of the problem hopefully it is related to the classic trunk wiring loom fault. Usually the fault occurs when you brake though, the short circuit backfeeds voltage into the ECU in an unexpected way and she gets upset. You state that it always occurs on heavy acceleration, which implies that the kickdown may be involved. I will have a search through the boards (this and the US one are a treasure trove!) and see what we can find. The transmissions are pretty tough, it is more likely to be an electrical gremlin than overheating from SPEEDING!!!.
Good luck, and please post any fault codes if you get them. The proper procedure is to read them, wipe the memory by pulling the EFI fuse for more than 15 seconds, then plug it back in and take it for a drive to get the problem, then read the fault codes again. The lexls site is a goldmine.
Good luck.