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Simple solution: Hide the Like button for the node you want to use up votes on. Or, custom development to strip it from the back end on a node basis. Remove current reactions either way. Then it's totally up vote in that node.

Edit: I might be mistaken, but you may be able to set "react to posts" permission to Never (or No) on the up vote node for the Registered group, then remove existing reactions. I'd have to double check node permissions to be for certain though.