Need shallow grooves in wood, *lots* of shallow grooves in lots of wood. At
least 48 in each side of dozens of 16 X 24" pieces of plywood and almost as
many boards grooved on only one side.

It sounds like you need a gang saw.

Some brands of planers can be converted to use as a gang saw, like
this one:

http://www.woodmastertools.com/s/gang.cfm

There are also plans out there for making your own drum sander. I bet
you could redesign the drum on some of those to get closer to what you
want...

--Glenn Lyford