I asked in TGG they said that my KUL-TGG-KUL ticket (Z) would allow it but wasn’t needed (or indeed possible as there was no earlier flight). They couldn’t tell me about the KUL-SIN flight.

Took my bags to the check-in desk at KLIA was categorically told it was not possible as I was on a Z class fare. Having had a long day I couldn’t be bothered to fight and say that surely it can’t be due to Z class as my previous ticket would have allowed it and that was Z class. Now spending an eternity in the Golden Lounge instead.

Thanks for the advice and tips here and although my experience doesn’t clear anything up, it is at least another datapoint!