Then we have a new question on our hands as to whether stun just prevents you from initiating an action or if it can stop an action that is already in progress. I could be wrong about this, but I believe it would stop the Battle Fury, and here's why. During Step 1: Declare Attack, you must check to see if you can legally attack your target with the Battle Fury attack, and I would assume the answer to that question is "no" because you are stunned.
If we read the rules carefully, we can conclude that it would not stop an action already in progress.
Battle Fury text:
"The next time this round the target creature makes a melee attack, if that attack is not a Counterstrike, at the end of that attack action it may immediately make another quick action melee attack. This extra attack counts as part of the same attack action. Only one Battle Fury spell may be cast per round on the same creature."
Even if Battle Fury start from step 1 to through step 8, it is part of the same action.
Stun makes creature Incapacited.
Incapiced text:
"An Incapacitated creature cannot take any actions, including moving,
attacking, guarding, casting spells, or counterstriking."
That's the interesting part. Cannot take any actions, but the creature is not taking an action, it is already in its attack action since Battle Fury extra attack is part of the same action.
Now, the Step 1 text (and where you are wrong about being legally able to attack the target):
"Announce which attack you are using. If your creature has
more than one attack, represented by more than one “attack
bars” on its card, you must choose only one attack to use.
You must choose an attack whose action icon matches the
type of action you are taking (for example, a full action icon
will require the creature to use a full action to make that
attack).
Then, announce what target you are attacking. You must
choose a legal target for your attack:
If you are making a melee attack, the target must be in the
same zone as the attacker. If there are enemy guards in the
zone, you must choose one of the guards to attack (see
“Guarding” on page 29).
If you are making a ranged attack, the target must be in range
of the attack. A ranged attack ignores guards. All ranged
attacks have a minimum and a maximum range. The target
must be in a zone that falls within that range (see “Counting
Distances” on page 10). Also, a ranged attack must make sure
it has a clear LoS (line of sight) - see “Line of Sight” on page
17. All ranged attacks ignore steps 6 and 7.
Pay Any Required Costs
Sometimes you will have to pay an additional cost in order
to make an attack. For example, an enchantment may force
you to pay mana before your creature can attack.
You must pay these costs during the Declare Attack step, or
the attack is canceled.
If you discover that you cannot legally attack your target
during this step, you may cancel the attack and choose a
different target, or even take a completely different action.
Remember: If a Flying creature attacks a non-Flying object,
it loses Flying until the end of the attack. See “Flying” on
page 15.
If later during the attack you discover that your target is no
longer legal (for example, it has been Pushed or Teleported
out of range), the attack is canceled.
If the attacker is Dazed, at the end of the Declare Attack Step
he must roll to see if his attack misses. If it misses, skip to
Step 5: Additional Strikes. See “Daze” in the Codex."
Nowhere in Step 1 it require you to be not-Incapacited. The legality of a target is not dependant of attacker's condition.And for damage barrier/counterstrike, it all depends if you consider "attack" and "strike" to be the same thing or not. Personally, I would allow damager barrier/counterstrike to only hit once.
I think the intention behind Battle Fury was to grant the next attack equivalent of "Sweeping or Doublestrike", but they wanted to allow it on Full Action attack too without allowing 2 Full Action attack and they could not word it like "grant next melee attack either Sweeping or Doublestrike" because if the attack was already DoubleStrike, they wanted it to get a 3rd strike.