Standard pin router fixture & technique. A wide flat fixture that slides around on the table. Mount your laminated wood board on the top. Mount a cylinder on the underside for the pin to follow.
Here's how Jeremy cut nice round disks from Rocklite scraps, for the Mermaid Bubbles fingerboard inlays:
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The shapes above are the patterns glued into the underside of the fixture. He used normal pin router technique; multiple shallow passes, working down in depth. Leaving 1/16" at the bottom so the wood disc didn't go flying. Then he sawed them free with the bandsaw, and cleaned the flashing off the bottom edge on the edge sander. After he did a few of them, he got used to sliding it around keeping the pin in contact with the pattern. The discs were coming out accurately round and smoother finish than you'd get on a wood lathe.
To make knobs, you could first pre-drill the center socket holes in your rectangular laminated blank, and epoxy in the metal insert sleeves. Then the fixture has a 1/4" pin sticking up, lined up with the pattern underneath. Clamp the blank down onto the fixture, with one of the inserts on the pin. Rout it down to full depth in 1/16" steps, leaving that 1/16" at the bottom. Move the blank to the next insert.
You could also a separate setup to rout the domed tops of each knob, using a radius bit or whatever. Using a pin to locate the blank, centering on the insert.
And, the knobs don't have to be round. You could make them any shape you want. Just hand carve a pattern that goes on the underside of the fixture.
And, you could build the fixture so it has a pin on the underside that different patterns would plug onto. Build up an assortment of patterns for different size and shape knobs.
That's the beauty of a pin router. Once you've invested the time to make the fixture and pattern, it's very quick to pull it off the shelf and run a batch of knobs.