[whpalmer4]

Isn't what you are asking for equivalent to saying you want badges only to be shown on arbitrary contexts or projects? Also, are you referring to the badge on the app icon, or the badges on the main screen of the application? You do have some control over the former, but only which types of items (overdue, due soon, etc.) are counted, not enough specificity to do what you ask.

The easiest thing might just be to pitch in and help your team meet those deadlines before they turn into ugly red numbers on your screen :)