I will record our experience, just in case someone else asks a similar question.

Based on the previous answer we booked our taxi for 6pm, and it also took us an hour to get to the airport. When we arrived the airport staff were setting up the queue management ropes and the desks for the TK staff. They told us the desks would open at 20.00 (T-3.5). In fact they opened about 10 minutes earlier.

There are 2 *G lounges in KUL - SQ and TG. However they both close at 20.30, presumably as their last flights go out around then. Although we were *G in economy, the TK business check-in gave us two passes to the contract lounge that they use, which was nice of them. My *G card alone would not have worked.