Hi Josh,
Your last note above is probably about right. I believe there is a ~4 week period from the time the Daylight team begins a build of a Daylight release with the latest OSM edits and the time it is publicly released. This is the time in which the OSM data is being run through a series of integrity checks and fixes are being made iteratively.
Once Daylight is released as a PBF and OSC files, there is a ~3 week period where it is loaded, cached, and published as hosted vector tiles by Esri. While that is happening, the next release of Daylight is already well underway and nearing completion.
I agree with Bern that it would be worth reaching out to the Daylight team regarding your process, and we'll discuss with them as well. There might be some ways we can optimize the process to get your critical edits in more quickly.
On a related note, Esri is hosting a set of OSM feature layers (now in beta) that are being updated directly with minutely 'diffs' from OSM. These are not vector tile basemaps, but they are an alternate way to get access to the latest edits very soon after they are made in OSM, and could be overlayed on the basemap in a web map.
Cheers,
Deane