Ironic that you should use the term 'slop', since that's exactly how they avoid flying the same route across the Atlantic tracks for example (Strategic Lateral Offset Procedure).
Right now, it's the middle of the day (12:50p Central). There's a bit of a mix[1], but it's still predominately westbound.
The consequence of this is that most traffic will be separated by at least 2000 feet. Eastbound traffic will (generally) be at odd Flight Levels (so 29000 feet, 31000 feet, etc.) while Westbound traffic will be at even FLs (30000 feet, etc)[2]. This assumes RVSM airspace.
[1] I'm just looking at the transatlantic traffic on https://flightaware.com/live/