Use your 1/4" shank bit to cut a circle template on 1/4" thick material.smaller than juice groove.on your router table.Thank you, I haven't touched a router in years, so been doing lots of re-acquainting myself with routing.
The cutter is also 1/4". I thought that 2" was likely a bit long on a 1/4" since hardly anyone had them. Yes, I can find some 1/2" x 2" CL that aren't eye-wateringly dear, so maybe need to go that route. They all have cutter and shaft both 1/2". I wonder if heat will be a problem with a 1/2" cutter in oak doing all the stock removal (as I don't have a bandsaw).
I'm still curious about the use of a 1" CL for a 1.6" thick application, would have thought it not possible or maybe some burning long the shank?
Safer to use a 1/2 shank router with a template Guide (AKA guide bush) and straight bit to cut in portable mode. With a smaller Guide bush can cut the juice grove first and changing to a bigger guide bush cut then cut edge.
1/2" shank bit with 2" cutting edge that came with my router FREE is useful with guide bushes. But you can buy patterm bits that comes with a bearing.

(When the material is big and heavy, take the tool to the material)