Thank you for your detailed answer, it just came a few hours too late!
I took my time after the shower and made it to the SAM by 10. I actually liked the exhibitions, there were some really cool pieces! Then I wandered downhill towards the water, and in the end I had lunch at the Quay which definitely fit your description of a club a little too early

But I had some nice dumplings and hainan chicken at the only restaurant which actually had customers, and a waitress that did not speak a word of english. I' took it as a good sign. Also I saw Geoduck in person for the first time in my life. What a weird beast.
After that I was totally toast so I came back to the airport and I am now at the gold lounge waiting for boarding. Next time I transit through SIN I should probably pack my swimsuit in my hand luggage and just enjoy the pool!