In Logic, how do I control the amount of groove/swing when quantizing?

You need to use the extended sequence parameters. Accessible either via key command, or by double clicking in the regular sequence parameter area (left side of the Arrange window). You will find a value called strength there which will let you get in between the preset swing values. The range values also offer a lot of useful flexibility; but that's not specifically what you are asking about.

While in the Arrange window, just press "P". That's the default keyboard shortcut to bring up the extended sequence parameters.

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