Extrude 0.25in circle into square piece

Hello, I’m new to wood working so any insight wood be really appreciated. The goal: extrude a circle into the square wood piece 0.25inches. What I’ve tried: using a cove 0.5inch router bit on a palm router and a drill press. What is the best way to do this?

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White Oak bookshelf I made during the latest heatwave on the east coast

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What’s the next step?

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Possible warping on this style of tabletop?

I have a peice of furniture I made awhile ago in school things didnt turn out the best so im repurposing it and turning it into a low coffee table. The only problem is the pannels from the peice are 18 wide were the lenght is shorter than the width. The way it was build it could pull that off but in a coffee table if I made the pannel 2ft wide and 18 long could the fact that its made 6 boards cause the pannel to bow or cup significantly? Would alternating the grain direction of the parts of the tabletop mitigate this or is this just a bad idea.

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