Thanks Singapore_Air! My ticket does allow a free stopover. It's a LHR-CGK return with 2 free stopovers allowed, although I thought a stopover is only considered as anything more than 24 hours, and a transit less than 24h.

In order to change my LHR-CGK (initially booked as a direct itinerary) into a 72 hr stopover in SIN, I had to pay stopover tax. Would I technically have to do that for my return in order to call my short time in SIN a stopover (as opposed to transit) so that I can get my luggage out at SIN?