Thanks, Alfred. You concisely summarize EXACTLY what I did. Point as type (not multiclass), layer-filter (one layer, all entities; but it does the same if I manually select all the entities on the layer; all other layers are OFF), and that's it.
Except I get no entities selected.
If I go in and select each BLOCK on the layer (which is what I'm trying to export) and COPY that into another drawing and do the MAPEXPORT, it works just fine.
So why in one drawing and not another? In the copied-to drawing, everything is on LAYER 0. In the copied-from (original) drawing, all the points I want are on a single layer. BUT THAT IS NOT WHERE THE DATA IS! I had to go back and refresh myself on AutoCAD's arcana. Blocks are INSERT entities and these ALWAYS EXIST ONLY ON LAYER 0. It doesn't matter that what is being displayed (and what is selectable) is on a different layer; you HAVE to include Layer 0 in the export.
So I went back and did the map export from the original file, but this time told it to use Layer "0" as well as Layer "Level 15" and manually selected the points (blocks) as I had done before. But this time it worked. Because it could read the selected Layer "Level 15" entities from Layer "0" where the block insertion points live (even though they are not visible or selectable there).
I should NOT have to remember this because it is not intuitive. AutoCAD should deal with its implementation-specific details. If I'm selecting something on a layer and it is a block, then go get the reference and don't bother me about it. I don't care if it's on Layer 0 or in memory somewhere or on the disk or in the cloud; I DID NOT PUT IT THERE SO I AM NOT RESPONSIBLE FOR IT. Can you imagine how much fun it would be if I had to keep track of where AutoCAD was storing things in RAM?
In short, if it LOOKS like it's on a layer then it should BEHAVE like it's on a layer. Don't think I'm just picking on AutoDesk; Esri has their own arcana with ArcGIS (and it is just as inexcusable).