Thanks, all interesting. As regards SLOP:
(a) the first reversal turn occurred at or not long after the INGO VOR, but that's not on a designated Upper ATS Route as far as I can work out - and in any case, it's not in Oceanic airspace, it's in the Reykjavik CTA where there's full radar cover so why fly an offset?
(b) the second reversal turn was in the opposite direction - left then right. That would put the aeroplane on the left side of the centreline (if there was one) - so conflicting with anyone applying the standard right hand offset in the opposite direction.
(c) not long after the second reversal turn, we passed directly over opposite direction traffic 1000ft below us. That would suggest we were not flying any lateral offsets but were flying under radar control. Radar cover at FL390 looks like it is pretty much continuous between Scotland and Iceland, at least with SSR.
I wonder if this might have been an aircraft with a transponder failure, and the turns were radar identification turns?