Turns out that the problem of the cross-hatching being tucked into one corner of the square was due to the fact that the perimeter was made of dozens of tiny extrusion segments while the cross-hatch extrusions were done with two xy coordinates, one at each end of the cross-hatching. Thus overshoots accumulated while I was doing the perimeters that didn't when I was cross-hatching. When I got rid of the overshoots the extrusion looked much better.
I fixed that by editing the .xml file. Now I have to upgrade the firmware to do that on the fly. At the same time I'm going to back up and turn off the extruder between paths.
The foamboard seems to be working quite nicely.