The roots of Japanese are very sensitive to disturbance so the least disruption you can provide the better. That speaks to planting something sooner rather than later, when the roots have spread out significantly from the original rootball.

It is best to choose some sort of plant that requires minimal attention and no need for frequent division, etc. that may require cultivation in the root area. If you were choosing some sort of flat groundcover, you could plant closer to the trunk than I would recommend for something larger, like a perennial or small shrub. I'd still keep a reasonable distance.