The Labor Department has shown scant signs of progress on revising an Obama-era rule to expand overtime pay eligibility, more than a year after embarking on its mission.

The Trump DOL’s latest soft target for a proposed rule is January 2019, after initially aiming for a fall 2018 release. A federal judge shot down the 2016 rule, which would have qualified an additional 4 million workers for time-and-a-half pay. An appeal of that decision is on hold to allow time...