For digital posterity: I also received approval on April 30.
Also for digital posterity: I applied for the Post-PhD Research Grant. It looks like all the forms, procedures, and timelines are identical for both the Post-PhD and the Dissertation Research Grants.
Finally for posterity, as it seems other applicants may have similar experiences: Reviews were visible long before news of approval appeared, and they were not universally positive. I was surprised by some negative comments made by reviewers, which a.) asked for information that I felt I had clearly given in the application; or b.) seemed to contradict the stated goals of the W-G Research Grants. This leads me to guess that W-G doesn't simply accept the reviews at face value, but actually reviews the reviews.
Good luck to future applicants, and especially good luck to all applicants who will put in the labor of resubmitting.