Apologies for the necro, but I feel that this is just too interesting and ruthlessly practical to die off. Should it come to it, I may pick up and carry the thread myself. After all, !!science!! leads!
I have a few suggestions that you may be interested in following up on - I assume any additions to the Mountain Dwarf Cripple Force would be welcomed. Here's the first one. Although it would undoubtedly lead to a higher casualty rate, would it not be better to amputate the whole leg of your crutchdwarves? It would decrease the mass of the dwarf, increasing speed, as well as reducing the number of potential targets for an attacker. I demand efficiency! Although, technically, the time taken and number of medical dwarves invested may not be worth it, in your view. In any case, I'm not saying, "Chop the whole leg off now!", though. That'd be silly. Rather, I suggest systematically removing the foot, lower leg and and upper leg in stages.
First, your initial method removes the foot. The patient heals up under the care of your best leech therapists your best medical staff, before removing their leggings. Then they're thrown in the meat grinder again, and dwarves are poised to retrieve them the instant they lose the body part. Now, the most dangerous part. Remove the chainmail shirt. This will leave the upper leg exposed and ready for removal. Unfortunately, this leads to the other leg being a viable target for our deadly spinny-blade-things precise surgical equipment. Nothing I can do about that. Anyway, once the offending body part is removed, you have a faster, harder to incapacitate dwarf that is much more intimidating to the enemy. Of course, this stage is the riskiest, but should the patient lose both legs and somehow survive the experience (and not end up as what I like to call "coma patients", lingering in bed forever), they are perfect for my next suggestion.
Leg-o-less and Gimpli
I'm very punny. Now, for these dwarves, you'll want to remove both legs. I would suggest modifying the amputation schedule. Do each part at a time, as usual, but set it up so that you remove both feet before moving onto the lower legs, and so forth. Once these brave men and women are ready to wriggle and drag their bodies around, set them on the ancient, well-traveled path of the axedwarf. For combat, forgo the shield and give them a battle axe for each hand. Why battles axes, you ask? Well, they don't have many different ways of attack when compared to, say, a sword. We don't want these troopers wasting a move trying to stab a gobbo's pinkie finger! We want 'em to slice it off, and maybe snag the other three and the thumb along the way.
Anyway, these fellows aren't meant to be slow meatshields or tanky, hard to incapacitate distractions (although, if you can manage to get a completely limbless dwarf to be exactly that, I salute you, you glorious bastard of a scientist). They're kamikazes, shock troops. They wear barely any armour, if at all, as to increase speed. Their job is to enter the fray when it's at it densest (or if you're impatient and want to test the waters with some semi-expendable units) and turn the tide. Sure, they're slow. But it's hard to knock a dwarf out by shattering his shins when he doesn't have any. The dual axes will make these fierce warriors fell the enemy like trees. Legs should be easier for them to hit, for a start. Plus, they can occupy the same tile as another unit., meaning that one gobbo could be fighting off three attacks from the same direction. As their moveset is limited, they're more likely to grab a foe with their teeth to immobilise him, rather than catch-and-release-ing with another body part.
Now, how do we get them where they need to be? The solution? Minecarts. As the OP pointed out, dwarves take no damage from falls in a minecart. Now, assuming you have a system where you can control the speed of your minecart and gauge how far you need it to travel (and thus, the speed required), you can tactically insert troops where they're needed (blue emu was making a joke, but I'm deadly serious). Now, according to the wiki, "if a minecart encounters the end of the track or a T junction with no "exit" in its movement direction, it will simply leave the track and continue on its course in a straight line until it encounters an obstacle, slows to a stop, or encounters another (properly aligned) track." All we would need to do is create a track facing out into the world, a few z-levels above ground, with no designated stop. Admittedly, this would be a weak spot in our fort when it comes to flying creatures, but that can be easily countered. Anyway, we would essentially shoot these shock troops out of the fortress to just behind our lines (or to just in front of the enemy, if you're fond of preemptive strikes). Undoubtedly, this would have a serious effect on enemy morale - "Who the hell would someone willingly be shot out of this place? They must be badasses of the highest caliber By Armok, they've got no legs! If I get out of this alive, I'll tell Ulspa McKidSnatcher to rescue more beards from these monsters!" (ulspa is the goblin word for dagger, by the way, whereas dwarves use urist). You could even apply the minecart insertion to regular units, possibly using the carts to cut a swathe through the siegers.
The idea came into being after a Legendary axe-wielding dwarf of mine became a paraplegic due to a hydra damaging a part of his spine adjacent nerves. He was too slow to complete most regular jobs quickly, so I initially gave him a shield, his trusty axe, and the best steel armour available. He got a good kill count from that, sure, but he was extremely slow, and wasn't as useful as his other axelord friends when it came to off-duty jobs. I suppose I wanted him dead. I gave him the two axes and took off his armour, and sent him out to face a Bronze Colossus with his mates. He did quite well, swinging a far bit faster and slicing off both legs with an axe each. At that point, the colossus got pissy and crushed him. So yes, this can be used to make leg-crippled soldiers into valuable troops again.
Chompy and Friends
That's an awful name. This one doesn't exactly belong here, but it involves a surgical procedure. It requires a necromancer and a corpse, either donated by a hostile or a slabbed dead dwarf/soon-to-be-slabbed, not-yet-dead dwarf. Toss the corpse into the operating room and turn on the blender. Hopefully, the head should have separated from the body. If not, try again. The plan is to have at least the head separated. Basically, the body will be a tag-team - the head's hard to hit and can latch on to hold an enemy in place while the body goes to town on them. Plus, anyone they kill can be reanimated afterwards (or during, if you're willing to endanger the necro). An ever-growing army, which can be disposed of if required (adapting a spikefall pit is always a good choice if they're too strong for your military. Lure them in with a cheesemaker, then retract the bridges and watch as they enjoy the flight). I've been trying to make a way to have magma'd zombies stay aflame for extended periods, which would be !!fun!! in a fight...
I have other ideas, but this is already a wall of text...