If i understand correctly, you're trying to inlay a rectangle (5"x7") that's 1/4" thick into a picnic table. Is this correct?
Personally I'd not make a stencil because you'll likely never need that exact size inlay again, plus... it's a rectangle. I'd just clamp a fence to the table and run the router along the fence for each edge. Then chisel out the corners of the recess if needed.
To me the hardest part (which shouldn't be incredibly difficult) will be setting the bit depth. I could be wrong but I'm gonna assume this picnic table isn't perfectly flat on top because most of them aren't. So I'd definitely fix that if it isn't. Make the area where you want your inlay as flat as possible plus a few extra inches on each side. If you feel the table is flat then you shouldn't have many issues.
The plaque is aluminum so sanding it flush won't be an option. That's why i said a flat surface is a must. Once the surface is flat, carefully set your bit depth to the thickness of the plaque so it ends up perfectly flush.
If anything, going deeper than the plaque thickness might be an option, and you can always use shims of some sort under the plaque to level it off before you glue it.
Tapping holes into the back of the plaque and screwing it in from under the table could be an option for holding it secure as well.
Another idea is to inlay the plaque some amount below the surface of the table and cover with an epoxy of some sort.
I feel like I've said a lot, and a lot of it based on assumptions. I apologize if i misunderstood what you're trying to do.
Sent from my iPad using Tapatalk