Thanks for the feedback! They are indeed particles. It sounds like Unity has been making substantial improvements to rendering large quantities of prefabs, but some things just look better as constellations of billboard quads.

Here's a stab at illustrating the bits involved:

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class ParticlePlacer : MonoBehaviour {

	ParticleSystem pSystem;
	ParticleSystem.Particle[] particles;
	int totalParticles = 0;

	void Start () {
		init ();
		demonstrate ();
	}

	void init() {
		// Note: If you want to set up the system in the scene editor, this involves a bit of repetitive setup before things will work.

		// I think the minimum is: 
		// - Disable the emission module.
		// - Set simulation speed to 0 (unless you want the other forces/etc. applied).
		// - Assign a material.

		// Also, make sure the global/local space setting is what you intend.
		// (This determines whether the GameObject's transform affects the particles.)

		pSystem = gameObject.GetComponent ();

		// Here's an example of how one might set up a new system at runtime, if you want to go that route.
		if (pSystem == null) {
			pSystem = gameObject.AddComponent ();
			ParticleSystem.EmissionModule emissionModule = pSystem.emission;
			emissionModule.enabled = false; // Disable emission.
			ParticleSystem.MainModule mainModule = pSystem.main;
			mainModule.simulationSpeed = 0; // Stop the default particle gravity/forces/animation/etc from running.

//			// If you want to build everything at runtime, you'll probably want to adjust the renderer too:
//			ParticleSystemRenderer pRenderer = gameObject.GetComponent ();
//			pRenderer.material = yourParticleMaterial; // (If you don't set this, you'll get pink squares)
//			pRenderer.renderMode = ParticleSystemRenderMode.VerticalBillboard; // (Change this if don't want standard billboard particles.)
		}
	}

	void placeParticles(Vector3[] positions, Vector3 offset, float scale, Color32 color) {
		// For placing particles, the steps are pretty simple:

		// Build an array of particles.
		totalParticles = positions.Length;
//		pSystem.Emit (totalParticles); // If you want to configure everything in the ParticleSystem component, use this to generate the initial particle data.
		particles = new ParticleSystem.Particle[totalParticles];
//		pSystem.GetParticles (particles); // If you want to configure everything in the ParticleSystem component, use this to retrieve the initial particle data.

		// Edit/define each particle (e.g. with positions, etc).
		for (int i = 0; i < totalParticles; i++) {
			ParticleSystem.Particle p = particles [i];
			p.position = positions [i] + offset;
			p.startColor = color;
			p.startSize = scale;
//			p.rotation3D = Vector3.zero; // use rotation3d for rotating meshes (and apparently this prop is not a Quaternion?)
			particles [i] = p; // This looks weird, but it's absolutely necessary, because these are values, not references.
		}

		// Assign the array of particles you just described to the particle system.
		pSystem.SetParticles(particles, totalParticles);
	}

	void demonstrate() { // This is just for testing. (But it still looks nice.)
		List positions = new List ();
		for (int i = 0; i < 1000; i++) {
			positions.Add (Random.onUnitSphere * 5);
		}
		placeParticles (positions.ToArray(), this.transform.position, 0.2f, Color.blue);
	}
}