Also. any untamed animal appears to escape immediately upon leaving the stockpile if the cages' destination is a trade depot, otherwise the only things i ever see escape are 'thief' types or critters significantly larger than a dwarf (sometimes?)
Personally when it comes to disposal of my captured enemies I use the arena method. Unfortunatly yes it involves building and linking dozens of cage traps, thats why I got an army of mechs. In addition every cage ever built adds one more mechanism to the lever in my dining room, thing must be worth 40,000 dorfbucks already by itself.
Once the critters are all ready i open the cages and the marksdwarves stationed above do their thing. Because im nice i dont lock my arena so those not sniped make a beeline for the door, where the melee squads await backed by a long corridor of traps just-in-case. Stripping weapons first is key, leaving armor on hostiles is also very useful to maximize training. If doing this with beasts like unicorns then you can always put a butcher/tanner right outside to help process the corpses.
Butcher shops being cluttered and not hauled seems like a bug. check you got food/refuse stockpiles with space, people with hauling enabled, idlers. seeing as it works when you decon the butchers it sounds like a proper bug.
The other big advantage with trapping and arena execution vs just an impaling spike (besides free training) is that the notable kills all end up on dwarves and their weapons rather than some lever operated spike, this yields nice engravings and an interesting Legends Mode if you read that
Regarding FBs and the trapping of...
Heliman is right in his first comment that using a cave-in to stun a trapimmune monster will cause it to be vulnerable to cage traps. However, FBs, along with titans and clowns as randomly generated monsters are all both TRAP_IMMUNE and NOSTUN. This means they ignore cage traps and will not be stunned by a cave-in (though a direct hit will still be fatal).
The ONLY method for capturing these types of guys is to arrange for a cage trap to be webbed by a spider. None of the above are web immune and web acts just like a stun.
(This has been tested and proven, I managed to cage FBs, Titans and Clowns for use in my invader defenses. It requires obscene planning and micro-management if at all unfamiliar with GCS silk farming techniques)
It has however possible (and done) to 'trap' an fb without a cage trap. A series of raisable bridges to funnel him from the caverns to where you want him is key here, with a bit of work you can make a maze for him to live in and route seiges through it