The dnata lounge turned out to be well worth the short walk.
We got our blood flowing a bit, grabbed a small taste of satay with cashew sauce, and waited out our one hour layover in peace.

Thanks for the advice. Everyone here was right. All we had to do was show our DPS-DOH boarding 'stub' for entry with no question.

For anyone who's pondering whether to pay a visit to the dnata lounge, I say do it! Make the most of your one hour stay in SIN.