It seems that really the search from main page is doomed to not work for non-DL award flights. But going to advanced page, selecting schedule vs. price, then it does return some results. (Before, though, also the main page one used to work...seems to be fairly recently broken by the DL IT "geniuses.")

Thank you for the tip that need to use explictly by schedule (I already always only search OW, segment by segment) and not the one off the main page!