In answer to my own question, I've written a program to "vectorize" an ArcInfo Grid ASCII files as an ESRI shapefile with a single layer containing oriented polygonal grid squares centered at the points of the grid, with an attribute value equal to the value at the coordinates of the centroid. The program (still under development) is available on GitHub. An example of a map produced with the program is on CartoDB (it might not be for long). Perhaps one could have done this in GRASS. Space for detailed answers in this vein is provided below.
In case the map has to be taken down, here is a screen capture will be available when this community awards me 10 reputation points. For now, it is commented out.