For the record: Another user pointed out to me that Overpass has a separate “map” API endpoint designed to simulate an area download from the OSM API. Even though I can’t use this endpoint to query the data at a previous time, I can still copy the underlying Overpass query that it is using as a basis for my modifications:
[bbox];(node(bbox);way(bn);node(w););(._;(rel(bn)->.a;rel(bw)->.a;);rel(br););out meta;
Careful comparison of Overpass’s query to my query above indeed revealed an edge case in which Overpass’s query correctly matched the behavior of the OSM API and mine didn’t. So anyone finding this thread looking for a way to simulate an OSM API area download using Overpass would be better advised to use the query from the Overpass “map” endpoint than mine.