You can publish the NEAR tool as a GP Tool. Portal for ArcGIS has the Find Nearest tool available OOTB.
The Near GP tool didn't work. It fails with schema is read-only error even when the near fields already exist. It also appears I would have to publish the GP tool once for each different input feature class.
The Portal tool might work. I don't have Portal installed currently so I'm stuck with my current solution.
without prepare the data (Quadtree ect.) with structure precalculated you could trivially increase the radius of the circle until it intersects at least one feature and then loop only on these. I do it for example with a soe.
This is close to what I do currently. I start with a radius that is likely to return 1 feature, then double the radius until at least 1 feature is found, finally iterate the results to find the nearest.