Just had one made the original way with lemon balm syrup - our local is a fancy country place that grows a lot of its own produce. Including lemon balm, and syrup or cordial is easy to make. No gin as this was a summer lunchtime offering. Very nice as a garden cooler.
The gadget for making these is a nutribullet. Blend the fresh peach (or nectarine) with a handful of ice, lemon juice to taste and a tablespoon or so of the fizz to loosen the mix. You can then pour the rest of the fizz into the nutribullet and stir gently if necessary before serving. Gives exactly the right fluffy texture.
Incidentally I have seen in various recipes that the peaches are cooked first. This works perfectly with ripe uncooked fruit.
Does 'freshly extracted carrot juice' require a juicer, Nutribullet, or some other piece of equipment usually found in the back of the cupboard of someone who went on a 'detox' after Christmas :)