Hey motorstereo,
I need some clarification, please.
You are using a router with a 1/2" collet, correct?
And your router bit has a 1/2" shaft?
Wondering why you are using an adapter and the 2" block?
In your photo, there is a lot of shaft exposed which will certainly cause chattering.
In my shop,this is what I would do:
Make a template out of a 3/4" x by maybe 6" square piece of plywood.
Cut, sand your radius on one corner of the template.
Pencil the radius on all 4 corners of your shelf.
Jigsaw the excess material on all 4 corners of the shelf, leaving 1/8" of material to the line, at most.
Screw the jig to the bottom of the shelf, with countersunk flathead screws (you can putty the holes later-they won't be seen underneath.)
Obviously, flush the edges of the template to the edges of the shelf.
I would probably clamp the template to the shelf for installation with the screws.
Screw holes in the jig would be 11/64" clearance.
Pilot the shelf with a 1/8" bit through the jig and install the screws, remove clamps.
This will keep the jig from walking as you install it.
Since you have a top-bearing bit, clamp the shelf face-side down on the bench, overhung obviously so as not to route the bench.
Here is the tricky part if you have never done it (practice on a scrap piece or 2)
BACKCUT with your router-
In other words move the router in the opposite direction that you normally do and nibble away at the excess material, little by little.
This is not an exact science...and feels entirely wrong, but it works.
You certainly want to have a firm grip on your router and have your body of to the side of the cut which you would do anyway.
For the finish cut, run your router in the normal direction.
The basic challenge is that you are trying to remove a lot of material, as you know.
A single pass could probably be done on an overhead 3-phase Onsrud industrial router-but guessing that you don't have one of those...
Hope that this is helpful.