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I’m working on a rolling lumber cart and I need to cut a dado the full width of a sheet of plywood. I figured the easiest way would be to clamp pieces of wood and slide the router between them rather than making a jig like was described in the bookcase thread. Am I right in still thinking that?

That's probably how I would do it. Simple, easy and quick.

First time I did that, I used plywood router bits.

The second and subsequent times, I used regular bits and made two passes.

Why? Plywood is almost never the thickness of the dedicated plywood bits---either thinner or thicker. Making one pass and the ply is floppy sucks!!

(11-27-2019, 05:32 PM)stoppy Wrote: [ -> ]I’m working on a rolling lumber cart and I need to cut a dado the full width of a sheet of plywood. I figured the easiest way would be to clamp pieces of wood and slide the router between them rather than making a jig like was described in the bookcase thread. Am I right in still thinking that?

I have done a lot of wide width dados and rabbits. I found the easiest way for me was to elevate the sheet vertically about 18". I use one straight edge and position it to the right of the dado. I set the depth and rout from the top of the sheet down. One pass for a 3/8" or less depth of cut.
I lean the sheet against the wall as it sits on two low trestles with a scrap screwed to each trestle to keep the sheet from kicking out. 
Very difficult for me to reach across a sheet 4'-0" wide, that's why I prefer to rout from top to bottom.
mike

I run continuous dadoes down the length of plywood sheets fairly frequently, so that I know I will end up with the dado in consistent locations when I subsequently chop them up. I use the back-side of a long Festool track that I clamp my Dewalt 618 to. I also follow the same approach as K.L in doing a two pass cut with a narrower bit, because plywood sizes are truly random these days.

One more vote for the 2 pass method, since plywood is now variable thickness. As for technique, anything mentioned above will work very well including your original approach.

The best way I've seen is to make two wooden "T-squares" and put one on each edge of the piece you want to dado.   Insert the plywood you want to fit in the dado and slide them together.   Then put a top-bearing flush cutting router bit a size smaller than the plywood (e.g., 1/2" for a 'nominal' 3/4" ply).   Run up one side and back the other (left to right on the bearing side).   The T-square provides accurate dado width and provides some protection against chip-out.

I built a Saw track and included a sled for the router. The router sled can be adjusted in and out to align bits of different sizes exactly to the edge. I do have the plans for sale on my site.

But for a one-off, your two board plan is perfectly adequate.

If your outfeed table for the TS is long enough. That's the way I do it. Not bragging, just glad I have the space & outfeed support. But the way you describe is good also.

Out feed table is not long enough. When I get a little better at this flat stock wood working I’ll remedy that.