tl;dr: I think you can reduce the delay to 8-10 minutes. Grace period edits are available for 5 minutes after post creation and search results can be stale for a few minutes afterwards, especially during system maintenance or outages.
And now the details:
The advanced search API ultimately runs the same search as would happen if you searched the site manually. This means that grace period edits need to be re-indexed before they become available. There's also a bit of result caching happening on API's side, but I don't think it's relevant here.
Search index updates happen roughly every minute, so I think you could get away with 5 minutes for the grace period duration itself + a couple minutes for the reindex.
Indexing runs on its own schedule and system load thatcould throw a wrench in as well, so you could potentially have an edit come in at the very end of the grace period that won't get picked up until a full minute + the time to actually update the index after that.
If the 15-minute delay is working well for you (which it sounds like it is) and is tolerable, I'd stick with that, but otherwise I think you could drop it down to 8 or 10 minutes without a loss of data outside of any unusual circumstances like an outage.