I'd either use a straight-edge clamped to the plywood to guide the router with a straight cutting bit. Depending upon the depth of cut it might take 2 passes, 2nd pass after adjusting the depth of cut, of course.
Easier would be get dado blades for your table saw. Take a cut, adjust the fence, lather, rinse and repeat.
I dk how well a router table could handle a large piece of plywood. You'd be wrangling that around a lot. Not only that, how do you plan on guiding the plywood? A typical router table, whether home build or purchased generally only ends up with a max of about 12" (if that!) Between the fence and the cutter.
Bottom line: If you have the router, I think your best bet is to simply use a board clamped to the plywood as a straightedge and cut the grooves using a straight cutting bit.