Field ack, dar, ammo and barracks can all be brought up faster by dropping supplies. If the zone base is yours it may only take 1 or 2 drops to bring them up.... if not, it could be up to 7 depending on damage.
Town ack can never be brought up by supplies, it's a timing issue.
Friendly troops sent to the map room to reset it does not work. The map room is reset after 10 min I think although I have heard 15 before. It definitively resets once a building or ack pops up. Quite a few times I have lost a map room capture to this.