I am certainly no expert, and what I have to contribute may not help at all.
However, I make objects mostly for my own use, and I believe that the 'pop-up' distance is related to the size of the object, and that may be why the objects you describe having an issue with are very small objects.
For my own objects, I add a single, untextured,inverted triangular polygon below ground level, and I seem to be able to control the pop-up distance according to the size of the object and the size of the polygon.
This is entirely my own experience, and I would be happy to hear from anybody who has more knowledge.