That puller should fit fine. Back the central screw all the way until it's recessed into the outer plug 1/4" or more. Then you can screw the plug into the crank all the way to the bottom of the crank. Now advancing the screw will push the spindle out of the crank.
If, for some reason you can't back the central screw enough, feel free to force it. That will push the pad off the end, buying you the added depth you needed.
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