Welcome to the Asana Community Forum @MishaUsesAsana!
Have you tried setting up a rule in My Tasks?
You could for example set the trigger for new tasks added which have a specific selection in a custom field drop-down. More info about rules in my tasks here.
Also this feedback request thread might be interesting for you.
Also if interested under Profile Settings > Hacks, there is one specific setting to move recurring task into the last section of My Tasks: How to Control Your Profile Settings in Asana | Product guide • Asana Product Guide
I hope that helps