Creating a separate CD timer for Battle Buff items such as Weed and the Velvet Mystery Gift would 

A) Increase the viability of Weed

B) Create opportunity for new items in the Battle Buff category boosting your other stats temporarily

C) Directly combat the Fertilizer shortage by giving more reason to have people doing Farm Robberies, and owning Weed Fields.

Moving Weed and the VMG into this new category could be a significant first step into attacking the current problems with Weed, and with the new production prestige update, would incentivise people to actually run their fields.

The velvet gift works off of medical cooldown for future reference!  Thought you should know.  I like this idea it would make weed actually usable lol 

This seems interesting/worth discussion, thanks for the suggestion!