I think it'd be interesting to give the Demoman a shield that, unlike the Targe n Charge and Splendid Screen, would actually block when you right click.
For example, it would still have it's own bar, however it would only be able to block X amount of damage. When used the person cannot attack and once damage is done to the shield it doesn't restore unless you return to a health locker. Once the shield takes full damage it will break and restore after 1 minute. It also should work only in the front of the player. The shield will however not FULLY block all damage, it would just take 80% of that damage.
I'd think of this playstyle as a type of tank, for pushing past defenses (or defending against multiple players) while still being faster than a heavy. Kind of like having a temporary Heavy being overhealed by a medic.
Edit: It should probably have some sort of cooldown in between uses as well as to not be used to annihilate people 1 on 1.