Well, if you're interested in doing a speedrun, rerecorded or not, might as well help you get things started!
Here's what my plan for the first hour or so of the game was:
- While in the pirates' cave, fight a group of Steel Bats, giving you 9 EXP (this is almost always the first battle you fight once you enter the cave)
- After you get Faris and the ship, go straight to the Wind Shrine. On F4, pick up the sword in the chest and equip it on Galuf - this allows you to kill the first boss before it hides behind its' wings.
- After you get your first set of jobs, immediately switch to Blue Mage x3/Thief, and let anyone but Faris be the thief. Head to Tule Village and fight the monster-in-a-box in the chest in the Beginner's House (1x Goblin), learn Goblin Punch, then kill it to level up to 2/2/2/3. Afterwards, buy Fire, Ice, and Bolt at the Magic Shop, switch to Black Mage x3/Thief (this time, let Faris be the thief) then go on.
- The next boss, Karlabos, dies to 6 shots of Bolt.
- Anytime before the next story event on the Ship Graveyard, switch to Blue Mage x3/Thief (you'll get event-based healing mid-way through the ship graveyard). Start bombarding the next boss, Siren, with Goblin Punches (this ability does massive damage if the caster's level equals the target's). Immediately afterward, switch to Black Mage x3/Thief.
- While heading toward Carwen Village or the North Mountain, fight a pair of Tatus (they're weak vs Ice) to level up to 3/3/3/4.
- Go to Carwen Village and pick up the Ice Rod there (it's hidden under an underpass around the middle of town), then break it on the boss, Magisa, to kill her in one hit, and win a Whip.
- Follow the story to Worus Tower. Right before the next boss (Galura), change to Blue Mage x3/Classless (let Faris be Classless), and equip the Whip on Faris. Now, let Faris keep Galura paralyzed while the rest of them beat up Galura with Goblin Punches (Galura is level 3). Afterward, switch to Black Mage x3/Thief.
- While heading toward Karnak, fight any Wild Nacks you come across (they're weak vs Fire) - they're very good EXP and the absolute best source of money in world 1, period. Build yourself up to level 8 or 9 or so (I haven't precisely calculated out the number of battles you should fight, sorry), then once you're finished head into Karnak itself. Buy one Ice Rod for cheap, then come back to buy five more (you should have plenty enough money to do so, if not, come back to buy the rest after Karnak Castle blows up).
- Go through the Steamship and kill the next boss, Liquidflame, by breaking an Ice Rod, attacking, then breaking one more Ice Rod. (I'm not certain if you can manipulate its' forms to be able to break two rods in a row without the second doing no damage, but I've never been able to do it in normal play).
- Change to Blue Mage x3/Thief, and escape from Karnak. Kill the next boss, Iron Claw, by breaking a rod, waiting for it to change, letting it use Death Claw (this is a very important spell), then breaking one more rod to kill it. Hopefully you'll be able to align the battles you fought on your way to Karnak such that when you win, you'll reach 9/9/9/10 or 10/10/10/11 or something similar).
- Afterward, go to the Ancient Library, and sometime there, learn Lv5 Death from a Page 64 there (preferrably during a Page 32/Page 64 battle). Then, kill Ifrit by breaking two more rods, then kill the next boss, Biblos, by using Death Claw then attacking.
Afterwards, I haven't done any real in-depth planning, but it shouldn't be too much harder to speed through the rest of the game. I wouldn't be surprised if a 5 hour run of it is possible. There's a way to kill every boss in the game in some incredibly fast way - most of them are in the boss battling guides or the low level challenge guides on GameFAQs.