Hi @Nick_Kawakami and welcome to the forum! I understand exactly what you are looking for and unfortunately the way Asana does auto-shifting dependency dates, it will only shift dates of dependent (or precedent) tasks if in moving their precedent (or dependent) tasks the task dates come into conflict.
Here is a past post around this topic which also discusses options with Flowsana. Auto-shifting dependency dates is now available on all projects! If you have any questions around Flowsana @Phil_Seeman is the one to ask!