Ha, kinda. You can get the parent brigade to release MTDs upon receiving appropriate authorisation from PJHQ - who may do so upon request from your customer organisation (you work for a DEC perhaps?). Basically make the 'event' an exercise, find a sponser for it, they'll release a DIN/DCI/Whatever it was, that gives soldiers (reg and reserve) authority to attend.. The Brigade might then approach DEC or whathaveyou for a refund for manpower etc.
I'm no expert, but something similar was engineered a little while ago. Alternatively hire the soldiers in a civilian capacity as contractors to apply their military experience.
Heh, if you have hierachy involved way above the Majors head then career climbers in bde may well sit up and be very helpful.