Props to Casey for solving this in just a few minutes.
First, take the object you want to move in a circle and place it into the 4 equal-distant cardinal points, recording each position on the timeline exactly 2 (or x) seconds apart from each other. Then create the fifth position by copying from the original keyframes to complete the rough circle. Use exact numbers for x position and y position - do not try to just eyeball it.
Hint: For this exercise I find it easier to move the object to the most distant Z position rather than scaling down. This will give you more information to use in the Curve Editor.
Load the X-position into the curve editor.
Make EVERY OTHER keyframe a bezier curve. Leave the other points a standard linear curve.
Load the Y-position into the curve editor.
Make the opposite keyframes a bezier curve. Leaving the other points a standard linear curve.
You do not need to adjust the handles on the curve point at all.
Screen capture for the X-Position:
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Screen capture for the Y-Position:
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