The technique is simple in theory: take a single layer, apply time remapping, find the frame where the end and start of the motion are close enough that the cut disappears. In practice, finding that frame is where most of the time goes.
This version took about 40 iterations before the loop became invisible. The export is three seconds. At normal speed you probably won't spot it. At 0.25x, you can. That's close enough.
The interesting part isn't the loop itself — it's what kind of motion lends itself to this approach. Fast directional motion almost never works. Organic, oscillating, or rotational motion usually does. The motion here lives in that second category, which is why the technique holds.