Best unique ways to bolster team cohesion and esprit de corps?
It also depends on why you think it needs built? If there is an issue you need to focus on things that address that.
However, if there are no issue and you just want to build the team then I understand. Especially in the units you spoke of have personnel that are very independent otherwise they would not be successful. So start with a BBQ like they spoke of below - having everyone in a relax atmosphere gives a chance to talk and share away from the office.
Also, unique sporting venues everyone can do away from work, paintball, rafting, sporting events. Finally, don't discount traditional Army events to build team cohesion - plenty of Fortune 500 companies pay fortunes for the type of team building events the Army provides. Obstacle course, leaders reaction course, get your chaplain involved and most of all NEVER say Mandatory Fun - once you say that you already lost them.
Best of luck and let us know how and what worked best.
CSM OB