Use your collars. Lay out your desired opening on a sheet of template
material. Now determine your bit/collar difference for cutting. Say you're
using 1/2" bit and a 3/4" collar. Nail your fencing strips 3/4" away from
the layout lines. Now cut the pattern (it'll be 3/8" too large in both
dimensions), remove the fences, use your new template to cut your openings,
which will, of course be 3/8 smaller because of the bit/collar difference. .

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I'm building blast gates.

I need to cut some clean 6-1/4" (or thereabouts) holes. Ideally, I'd
cut through the 3/4" + 1/4" + 3/4" at the same time to get a perfect
fit.

I'm guessing the router is the way to go, but can you lead me to some
hints and tips, pictures, or other suggestions?

Thanks,