As written, using improvised weapons is a Melee attack. However, how about allowing them as a Brawl attack under certain conditions.
1) The improvised weapon must be within Engaged Range from the combatants at the moment the attack is made.
2) The attacker must spend a Maneuver to interact with the environment immediately prior to the attack.
This doesn't represent picking up a rock and hitting someone with it - that would be Melee. It represents slamming someone's head into a rock or slamming them down on a table or shipping crate.