[Lizard]

If I understand you properly, OmniPlan should do exactly what you describe.
You've set the project start date to August. You don't have task or group start dates locked.
If you're using leveling, you might try re-leveling to see if that works it lose.

Also, it would probably really help to send us your file and point out specific tasks that aren't behaving as you expect. (If you use "Send Feedback" from the Help menu while your doc is open, you can attach an anonymized version of it.)