How to create proper 'duplicates' of ways in JOSM?

Nope.

You can make 1 and then easily duplicate it with control+D and then use rotate (hold control+shift while using the select tool) to position the duplicate.

For tagging you could use a search like "inview building" to quickly select them all, maybe with something more selective than building.

This is something I've wanted, but it isn't possible in OSM because of the fundamental properties of the data model.

My use-case is with hundreds of houses built to the same plan. After initially mapping them I realised that I had a minor error in the geometry (the set-back from the baywindow is too large). Correcting this on hundreds of ways at a wide-range of orientations is not only tedious, fiddly work, but is also to retain exactly the same geometry for each element.

Really to manage this OSM would need some kind of object model. It doesn't: only tags provide the information that something is even an area, let alone a building or a particular type of house.

Instead you need to break down how these objects are described in such a way that one can create a strategy to manage them in the way you describe.

For tags this is fairly straightforward. Tag the original element to be copied with a tag which will allow you to identify it and its copies. This may be a 'private' tag: i.e., one not (widely) usable by other contributors & consumers. I tend to use my username as the base for such tags, e.g., SK53:building:001. As long as no-one deletes the tag it should be possible to select all the elements and manipulate their tags as a whole.

For geometries I don't think there is anything directly available. The Replace Geometry option of JOSM would be a place to start. What would be needed is a means to identify the orientation of each individual element. A new geometry could then be rotated to that orientation, with perhaps the same centroid or other identified constant control point for the existing object and then used to replace the geometry keeping the tags intact. There is undoubtedly devil in the detail: defining a suitable orientation operator, replacement geometries may have different centroids, buildings attached to other elements, etc. However the individual steps are conceivable operations within JOSM.