Your technique is poor and you need to fix it. The actual rope has nothing to do with getting up. A wakeboard line (assuming it is no stretch) will be more taunt under extreme loads. Getting up is not an extreme load. Your slalom rope needs to have some minor stretch in order to help you on the course.

Your rope is too old to justify skiing with it. Buy an new rope. If your slalom rope breaks under load (which is when it will), you can have snap back that can damage your boat, you, and/or people in the boat. Normally it will be the driver getting hit in the head. I have been in a boat with a snap. Fortunately, it had a tube on it which protected everyone in the boat.

Work on keeping your knees up to the chest and push down as soon as the boat pulls. Keep the ski tip out of the water at all times.