The main question I have is what does "not as well as I wanted" mean-- if you scored just at the mean or barely above on step 1, it might be worth improving your score. If you scored below the mean, definitely. If you barely passed, 100% take it in August, the early date. A lot of it will depend on how you did on your 3rd year clerkships as well. If your clinical grades are phenomenal and you got above the mean on step I, I would sweat it too much. As mentioned above, some programs don't even look at apps until they get the deans letter. So you could send in your step 2 score as an addendum and be fine.
Can't count out that it's possible to not do better or do worse on the step 2. I took it "early" in order to improve my score for ERAS submission-- got the EXACT same score the second time around. AND on step 3. It was comical actually. I got above the mean but not tons above.
So weigh your overall application and decide. Noone cant ell you exactly what to do here, only what we know from experience, since only you know your entire portofolio. In peds, Step I isn't a dealbreaker unless you get below the mean or your clerkship scores arent good. Good luck.