My effort:
Heavy Unlockable, Minigun slot:
Tactical Shield, named "Iron Curtain"
Last unlockable. 22 achievements.
This shield has no attacking power. Instead, when wielded, the user may press secondary fire to bring it up. There is a delay slightly less then the spinup in bringing the shield up, during which he is still vulnerable to all attacks. This makes switching between weapons and equipping at the right time a skill the heavy must truly master, and prevents him from blocking and immediately firing back.
Once equipped as so, the heavy takes no damage from frontal attacks. The shield is large enough to cover the entire front of his body, so headshots are not a possibility from certain angles. However the Heavy moves at the same speed as when firing Sasha, and has a limited FoV (not quite to the extent of the Sniper, and in a rectangular shape) and so is highly vulnerable to backstabs. Additionally, he can still jump with the shield equipped.
However, as an addition, the heavy will be granted a frustration meter, as the heavy does not like to be away from mowing down enemies for long. This is a visible form of the heavy's critical hit percentage, in the same form as the ubercharge. This could be called, for example, his Comragery (play off of rage+comradery if that wasn't obvious
) When the heavy's shield absorbs damage, this meter is added to at a rate such that blocking a level 3 sentry for 20 seconds could increase it to 100%. The meter also decreases naturally, 1%/second with an additional -16% per secondary weapon shot/melee weapon punch. This could also be visible in the form of the Iron Curtain heating to a glowing red as it absorbs fire, if the modeling resources were available to do so.
This weapon will significantly change the heavy's role both offensively and defensively, However, it does so in a way that enforces the idea of him being the "heavy" member of the team, without encroaching on other classes' abilities.
The heavy will now fit the "defensive" class specification he's been assigned better. His job will be to lead his comrades into battle, pushing through tunnels against sentries, jumping in front of rockets and stickies and saving his teammates at every corner. He can tackle ill-planned ubercharges but will not be a prime target for friendly medics; with only his secondary and melee weapons to fight with, he would make a poor uber and he doesn't require the health buff they grant to do well on his own. An intelligent heavy will make use of the skills you mentioned, such as bringing the shield up at the right time, predicting when damage will be incoming, while watching out for flank attacks, as he is now very vulnerable to these. Additionally he will have to learn when to drop his shield to switch to the shotgun and devastate the enemy. If he participates well in the team and defends his teammates properly, a solo heavy will quickly build up the crit power to rampage through 1-on-1 encounters. A good iron curtain heavy will constantly have to consider whether or not to have his shield out and up.
This will have a variety of gameplay effects for such a small change. For example, offensive engineers will now have a new friend and a reason to be on the battlefield. Imagine Dustbowl stage 3-point 2. The attackers are trying to round the last corner, but spam and well-placed sentries have them locked down. In comes a heavy wielding the iron curtain on the attackers' side. He raises his shield, notifies the two engineers behind him, and jumps into the fray. He pushes forward onto the lip of the bridge and rotates his body to varying degrees as attacks come at him. Meanwhile the two engineers have followed single file. One places down a sentry as the other helps him set it up. Together they are able to get it to level 2 quite quickly. The heavy notices his Comragery is now at 85%, a significantly high level. The engies shout their okay and the heavy drops his shield, jumping aside as the fresh sentry decimates the defenders before succumbing to the other sentries. In the meantime the attackers have pushed forward and the heavy joins them with his shotgun, expelling critical hits at the defending engineers. Of course, if the other team was clever, they would have had a backburner or spy on that heavy in no-time. It's a powerful tool but not without its limits. Stickies in a tunnel will not be brushed aside by the shield, so a demoman facing an oncoming iron curtain just needs to wait til the heavy has passed his stickies.
Of course there are numerous other situations in which it would be useful, but that's up to the players to elaborate upon.
Total resources:
Animated (progressing from cool to redhot) Shield model and static viewmodel.
Metal dinging noises.
Comragery coding. I figure this would be a combination of adapting the current critical hit % modifier into a viewable meter, and then adding to it based on the amount of "health" that is being taken off of the shield's hitbox. Probably the hardest part.
Shield coding. Adapt some leftovers from CS or CS:S and combine it with the spinup coding on the minigun.