OP here. So I came prepared and had only a 2 oz bottle of contact lens solution for my transit thru SIN. Went thru just fine as did liquid prescriptions.
But wouldn't ya know it, they found something else to confiscate - a corkscrew. Apparently not allowed in SIN, but allowed EVERYWHERE else in the world, including LAX, SFO, SNA, ONT, BOS, DEN, IAH, SJC, CUN, FRA, ZRH, DPS, and BKK (to name just a few).
When she said it was not permitted, I said fine, just throw it out (it was a freebie). But no, there was a whole process, a form to
sign, and the airline (SQ) had to be involved. Once it we finally got over to the BP check station with the oh so dangerous corkscrew, they wanted to check it thru to BKK (next stop, but we were transiting only). I told SQ to just throw it away which they happily did.
In addition, while looking for the corkscrew, they also asked if I had glasses in my carry-on (as in normal eye glasses). I said yes and pointed them directly at the glasses. They then proceeded to RIP thru my toiletry case (pill bottles, glasses, toothbrush, etc). Not a gentle pawing thru, but literally tearing it apart to the point where it took me a while to actually get everything back in (with no offer of help - which I would have declined anyways - but still). Apparently my battery operated nose hair trimmer also peaked their curiosity and required a rigorous manual inspection
Seriously Changi, why do you have to be different than EVERYWHERE else on the planet?

I'm surprised they haven't put full body scanners everywhere to make security there even more of a nightmare.