How to snap copied region while maintaining the right rotation?

So I’m doing retopology, and in my case one region repeats three times, except they differ in rotation. So I tried to retopo one thing, then copy it and…
Well here’s the problem: how do I snap this to another identical region, so it would snap with it maintaining the right rotation?

Here’s the model I’m working with (you can see what part is repeating itself: those three wormy-like extruded thingies:

So basically I want to retopo one part, and then copy it onto the rest, but I can’t figure out how to snap it with rotation, even though I tried using “Align rotation with the snapping target”, but it made a mess, but maybe I set the wrong settings.

Any ideas?

Maybe this way:

  1. Duplicate the extrusion
  2. Rotate it by 120deg on Y axis
  3. Repeat 1 and 2
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To align rotation…

Snap the 3D cursor to the desired center of rotation.
Change the pivot type to 3D cursor.
Change snapping to vertex mode, and active element.
Select the geometry you want to rotate into alignment.
Deselect and re-select the vertex you want to index into alignment with a vertex on the other geometry. This makes it active. (In default theme, it’ll be white instead of orange. Keep in mind the other geometry you want to move with it should still be selected and highlighted in orange.)
Now rotate about the desired axis, and if snapping is enabled the rotation will index the active cursor to the nearest vertex on the outside geometry that the mouse pointer goes near.
Rest should be obvious enough.

Hope that made sense.