The Bebop Calisthenics aren’t supposed to sound the same and you aren’t supposed to view them as actual “lines”. The reason they sound different is because they start on the highest available chord tone for each fingering which is often going to vary from one pattern to the next. Your goal is to be able to play the entire arpeggio from the highest to lowest note (and vice versa) and learn to identify the location of each target note. To paraphrase, this is an exercise intended to develop awareness of target note locations in different pattern contexts, and how to properly precede the target with a given approach using the correct fingering.
If you try starting all of them on the same chord tone, you will defeat the purpose of the original exercise. It is true that you will maybe learn a “line” and train your ear and fingers to start on specific intervals. You can, if you wish, make this into another area of practice, but I recommend also doing the original exercise and training your ears to hear the the different target notes within a variety of contexts.