You repair it from the TOP of the sink.
1. If your description of the handle operation is correct that is how the faucet is SUPPOSED to work with you pulling the handles toward you to open them and pushing them away to shut off. BUT,
2. if you really want to reverse them, you need to remove the two stems and interchange them, then
3. Call 1-800-4KOHLER and have them send you a new stem, which now will probably be the hot one, but in any case tell them whether it closes clockwise or counter/anti clockwise.