This is one of the reasons that in my group, we flesh weapons out with attached aspects... nearly every weapon. It has yet to provide any disadvantages, but something like "Massive Damage" or, hell, "Elephant Gun" might be a weapon aspect. We treat these as permanent/semi-sticky aspects: usable once per weapon maintenance for free (I'll explain this next), and for a FP after that. For balance reasons, and as far as determining how effective a given weapon is, we consider each aspect permanently placed on a weapon to be equivalent to a +1 damage bonus.
So, a Weapon:3 Rifle with "Elephant Gun" and "Massive Damage" and "Hollow-point Rounds" on it is capable of doing a theoretical Weapon 9 strike to a target as long as it's an elephant (or something equivalently massive)... easy overkill to anything else, but costs FP to be able to consistently do that much damage... and is roughly equivalent to a gun that does a constant Weapon:6 (Base 3 + 3 aspects).
Similarly, we stat out a Barrett .50 Cal as Weapon:5 with "Massive Damage" and "Long-Range Scope." Other possible non-lasting aspects include "Cold Fire Ready" and any number of custom hand-loaded rounds (these latter handled through a craft check to actually place a sticky aspect on the weapon...). Given a marksman who's willing to do this prep, and takes time to aim ("In My Sights", "Steady Breathing", "Calculated Shot"), a sniper can easily do CRAZY massive damage on a single shot... and that's not unrealistic or game-breaking, IMO.
The scope can be tagged for extra accuracy, or add to range (negate range penalties)... but as my ex-army marksman buddy can confirm, firing a gun changes how it fires. It heats up the barrel, leaves carbon in the barrel that can affect accuracy, shakes the scope slightly, etc, etc... all minor effects, but worth paying attention to.
This #1, explains narratively why the aspects only get one free use (FPs after that represent some measure of skill to adjust for the change), and #2 why weapon maintenance resets that usage (cleaning the barrel, dialing the scope back in, cold-firing it brings all this back into play)... it just has to be represented in some way- even if it happens off-screen.
For melee weapons, think about how you hone the edge of a blade for extra sharpness. Those edges don't keep even past the first cut. The most common melee permanent aspects I see are "Concealable," "Honed Edge," and "Heavy." (each with what I hope are obvious uses, and occasional drawbacks).
Concealable 'goes away' because you've lost the element of surprise (unless you're getting weird with slight-of-hand), honed edges wear off, and heavy weapons tire you... all require FPs, or a chance to rehide the weapon, rework the edge, or rest.
Would something like this work better for killing your elephant?
It's not catch- doesn't completely bypass that extra meat, but it goes a long way towards helping.
An elephant without Toughness can be killed from ambush by an unarmed Pure Mortal Chest Deep martial artist, without the use of FP or fancy tricks. This is mildly absurd.
An elephant without Toughness can be killed by a gang of ordinary people throwing rocks. Again, absurd.
But more important than that is this: the difference in effectiveness between a pistol and an elephant gun against an elephant is greater than that indicated by the threeish point difference in weapon ratings. The Catch simulates this elegantly and effectively.
I agree with you on almost everything, sancta, but must point out this:
I think an elephant getting taken out by a gang of ordinary people throwing rocks isn't that absurd... after all, being driven off is a kind of taken out,
and is completely reasonable. If the gang has it's heart set on killing it, and the GM is uncomfortable with that, this is where negotiating the take-out comes into play.
Also, I'd say my solution effectively and elegantly solves the problem without needing to go into catches.