>  Advice on how to eliminate the extraneous cells (and clip the raster to
>the nearest cell boundaries of the vector map) is greatly appreciated. 

see http://grass.osgeo.org/grass64/manuals/html64_user/g.region.html

align=name
    Adjust region cells to cleanly align with this raster map

vect=name[,name,...]
    Set region to match this vector map

to set the region boundary to your analytical vector: i.e.

g.region -a rast=dem_east vect=analytical_boundary align=dem_east

then r.mapcalc "dem_east_vect_analytical_boundary = dem_east"

?
Helmut

-----
best regards
Helmut
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