EWR-SIN-EWR would do it, provided the EWR-SIN flight goest east over the Atlantic (as it did when I took it due to very favorable winds on that route) rather than north literally over the pole. In terms of flying time, it's less than 18 hours EWR-SIN and less than 17 hours SIN-EWR, for a total of 35 hours. The ground time between flights is approximately the same in both SIN and EWR, about 5 hours, so even if you count that you're well shy of the record set back in 1980.

JFK-FRA-SIN wouldn't do it, because it goes back the same way, never traverses the Pacific. SQ's other roundtrips, include the nonstop to LAX, go over the same ocean both ways and therefore don't circumnavigate.

TG's New York Express BKK-JFK and Bangkok Express JFK-BKK have flying times of about an hour less than SQ 21/22 because Bangkok is not as far south as Singapore. BKK-JFK naturally goes trans-Pacific. I presume, though don't know, that JFK-BKK goes trans-Atlantic, at least most of the time. So it could qualify as the fastest circumnavigation. It's downtime is about six hours at each station, which cancels out the shorter flying time.

Can't think of any other flights that potentially circumnavigate.

But the other thread linked above has a few, such as JFK-LHR-NRT. Much fewer miles than a SIN or BKK routing, so it takes slightly less time. All depends on what you consider circumnavigation, but EWR-SIN-EWR and JFK-BKK-JFK are the only ways to do it with one stop at present.

And I don't know about how "regularly" the subject is discussed. That other thread, at least, was more than two years ago--before SQ started the EWR nonstop and TG started its nonstop. Now, I did bring up circumnavigation in a thread discussing SQ 21/22 earlier this year, but it wasn't strictly on that subject. And as some pointed out, SQ 21 doesn't always go trans-Atlantic.