Pyro: While I don't agree with giving Doll gun skillz, I will point out that, if you do, she's two divisions too low (initiative 2HKO) and obviously splatters Garr.
Super: The only game where Pokemon sleep can "lock" a target is RBY, in every other game the target gets an action the moment they wake up (and sleep can't be reapplied to a sleeping target). This matters because (a) you don't vote on RBY, and (b) RBY Butterfree loses this match real bad anyway. That said it's possible FRLG might win anyway, I'm not looking up its damage there to figure that out.
I'm using the lower average for Garr for now. I could be argued on this, but Garr missing the 4HKO with the Beast Spear just feels kinda intuively wrong to me.
Garr (BoF3) vs Gen (Child of Light): I am inclined to agree that paralysis is the best path for Gen, it essentially buys her two turns with each use (a bit less, but knockback makes up the difference), and she 5HKOs average so that's... something? Feels less completely pathetic than the other build. Anyay, Garr can 3HKO her without hitting the limit range, which is bad for her, but he is slow. She only 7HKOs, though, so even with paralysis doing some wrecking I'm pretty skeptical she can win this.
Garr vs Butterfree (RBY/FRLG only): Fire physical with Beast Spear OHKOs. Wow.
Garr vs Locke (FF6): Garr 3HKOs Locke. Locke gets in 4 turns before that happens, and even assuming he's forced to take his double after Garr's first attack that's too much damage.
Garr vs Kain (FF4): Kain 7HKOs, Garr either 6HKOs (and is easily 7-6ed) or 5HKOs with Beast Spear and is now effectively 6HKOed (and 6-5) due to backlash.
Garr vs Gong (SF1): Gong has a 9HKO, Garr has a 4HKO unless he wants to eat backlash. Each shot of Heal 3 can erase 2 Garr attacks, so Gong loses on Garr's 10th turn and gives up three of his own attacks. The question is, does he 12-10? Yeah. Sad.
Garr vs Racially Insensitive Wizard (FF1): Garr 2HKOs with the Beast Spear to me... but Break probably rises to barely turn 2 against his MDef.
Garr vs Marcus (FF9): Marcus 5HKOs, Garr 4HKOs... and yeah, dat 5-4 exists.
Garr vs Aeris (FF7): If Gong can manage it...
Garr vs Lissa (FE13): Garr can actually 2HKO with Beast Spear here, too, so he just needs to survive three Lissa attacks. Thoron... 3HKOs, though may miss. Of course, Garr may miss too, have to think that balances.
Garr vs Tricia (SN): 60% spear weakness means Garr 2HKOs. Even with a counter in there I really can't see Tricia winning this.
Garr vs Doll (SaGa): Doll sucks. If you give her GlassShield she wins this, but I don't think I do, the argument for it is based around NG+ (unlike dark magic, which I do give her, it isn't possible to get her the Mystic gift, so it's no easier to get her Glass Shield than any other human). And yeah, Garr nulls draining, so no PowerGrab hype.
Garr vs Guido (G1): Guido is bad and should feel bad.
Labyrinthia (WA:XF) vs Gen (Child of Light): Gen... just misses the 3HKO to me. Still, paralysis, attack x2, paralysis, attack x2? Not sure if this outhustles Labby's second turn. Probably, though. Unless Weapon Guard works here? Nah, Gen's physical has a special effect, it probably doesn't scan as a "basic physical" to me.
Labyrinthia vs Butterfree (RBY/FRLG only): Don't think Butterfree breaks the distortion, and it gets OHKOed anyway.
Labyrinthia vs Locke (FF6): Locke has a 3-2. He doesn't even need low-HP powerups to 3HKO Labby.
Labyrinthia vs Kain (FF4): Lightning resistance.
Labyrinthia vs Gong (SF1): Labby, fortunately, just manages the 2HKO. Actually no wait, it doesn't matter, Gong vs distortion is failure.
Labyrinthia vs Racially Insensitive Wizard (FF1): Unlike Garr, Labby's MDef is on the right side of average, so status is turn 3 at best here, and Labby 2HKOs. She just misses being 2HKOed herself.
Labyrinthia vs Marcus (FF9): Marcus 3HKOs and halves lightning.
Labyrinthia vs Aeris (FF7): Uhhh Aeris can mess with her MDef a bit via her Umbrella/Princess Guard (20 spirit difference), while Labby has basically perfect control of her weapon. If Labby 2HKOs without triggering a limit, she wins. If she triggers a limit, she loses, and if she 3HKOs, she loses (Aeris 3HKOs faster). Though... actually, she can chip a little with her physical if need be, since Attack and Aim Down means Aeris probably whiffs on the opposite turn. So... Labby has a lot of ways she can win.
Labyrinthia vs Lissa (FE13): 3HKOs and counters, isn't OHKOed, goes first.
Labyrinthia vs Tricia (SN): The reverse of Garr! Typing means that Tricia completely crushes, here: 2HKOs and counters and is only like 4-5HKOed or something.
Labyrinthia vs Doll (SaGa): Doll vs distortion.
Labyrinthia vs Guido (G1): Guido is bad and should feel bad.
Labyrithinia 6-6
Garr 5-7 (... significantly worse if I use the higher damage average)