Although the barbarian was introduced in Advanced Dungeons & Dragons (1st edition) in the Unearthed Arcana supplement, they were tribal wilderness warriors more akin to rangers, and didn't have anything resembling the rage ability. It wasn't until Dungeons & Dragons 3rd edition that barbarians appeared with an ability with the actual name "Rage." However, there were earlier versions of the Rage ability that just had different names.
In The Complete Barbarian's Handbook (AD&D 2nd edition) there is the Brute class kit which provides a barbarian with the "Wild Brawl" special ability, which is introduced with, "When fighting without weapons, the Brute can propel himself into a berserk frenzy." However, "Wild Brawl" is mechanically entirely unrelated to Rage.
In the same book, the Ravager class kit provided the barbarian with the "Become Enraged" special ability, with which the "Ravager may work himself into a fighting frenzy, increasing his effectiveness in combat." Mechanically, an enraged Ravager hits easier and does more damage, is hit easier, is harder to damage, and is harder to charm.
Also in AD&D 2nd edition there is a Warrior class kit exclusive to dwarves in The Complete Book of Dwarves called the Battlerager, which is "a fearless warrior, able to create an insane rage within himself which increases his fighting ability and distorts his physical features," and therefore a dwarven barbarian in all but name. A Battlerager in "the Killing Rage" receives bonus hit points, bonuses to attack and damage, and an AC bonus, as well as being immune to charm-like effects, but may not stop fighting until there are no more enemies standing.
Similar to the Battlerager is the is the Berserker class kit for fighters in The Complete Fighter's Handbook (AD&D 2nd edition). A Berserker takes a long time to "Go Berserk", but once Berserk gains similar benefits and also can't stop fighting until every enemy is down. Notably, a Berserker isn't allowed to know their own hit points while Berserk!
The Complete Book of Dwarves was published in 1991, four years before The Complete Barbarian's Handbook; but The Complete Fighter's Handbook was published two years earlier in 1989, making the Berserker the first barbarian-like† character with an ability that is recognisable as a "rage" ability.
†Bear in mind that before D&D3, the actual barbarian class was restricted to humans, so fighter class variants like the Berserker and Battlerager was the official way of playing a non-human character that fulfilled the same class role despite not bearing the name "barbarian."
The common consensus on the function of mountain rage is that its increase in your size replaces your powerful build feature, as in your first alternative. That is, during a mountain rage you (assuming a typical Medium goliath) lose your pseudo-Large status per powerful build in exchange for true Large size. And then you get an extra +2 Strength above normal because reasons.
As for what the rules-as-written actually say, that would be closer to your second option there: it excepts grapple bonuses and weapon size increases from the benefits you gain from growing in size. And, from a RAW perspective, that would be the end of the story, without really caring about the bit that references powerful build. So you would gain other benefits of growing, including those that powerful build also offers, just because only grappling and weapon size were actually excepted by mountain rage. Generally speaking, rules-as-written tends to ignore things said after “since” because it doesn’t really matter why you get a particular benefit, and because it’s ambiguous and impossible to figure out what happens when those since clauses are inaccurate (for example, a stoneblessed character could count as a goliath and take the goliath barbarian substitution level without actually, ya know, having powerful build).
Best Answer
Looking at this thread, there are a few of rage-substitute class features that fit the style you want: - Berserker Strength (PHB 2, p 33): Lose rage. Gain a rage that activates every time your hp drops to below 5x your barbarian level. - Crafty Hunter (UA, p 58): Gain favored enemy, archery combat style, improved archery combat style, and greater archery combat style. Lose rage and indomitable will.
The best way to simulate Fezzik is with monk. Call him a brute, but the various unarmed attacks and some of the class features (suitably renamed) fit him quite well, especially with "Decisive Strike (PHB 2, p 51): Lose flurry of blows, gain ability to make one attack that deals double damage." and "Durable (UA, p 58): Gain damage reduction as barbarian. Lose speed enhancement bonus and bonus to AC (but not wisdom to AC)."
The best way to simulate He-man is with Ranger. He even has an animal companion and dual-wields.
The best way to simulate Ox, especially with his superhuman strength and durability is Psychic Warrior, fighter, or equivalent with... a depressing number of templates.
The best way to simulate Bamm-Bamm ... is with Psychic Warrior, his "hitting the floor and causing it to shake" is a great reflavouring of "Shout"
The essence is found in OOTS, where your job "title" doesn't come from your class levels.