A few web searches turns up the information that there's evidence that they used to be stocked on game shoots and estates, alongside the more familiar suite of deer, pheasant, partridge, grouse, etc. This page, The Shepherd's Wild Turkey, describes how they were traditionally hunted (with greyhounds, young birds only, as an adult male could seriously injure the dogs) and then how, with the introduction of game shoots, they were shot out and became extinct (doubtless while the hunters whined that such large, slow moving birds were "poor sport", ack thpt).
Obviously the slow maturing, lekking habits, wide ranges and nervousness are barriers, but I'm not really seeing anything that would really prevent farming. Feed supplementation, penning, artificial incubation and chick rearing could produce a small farmed population, whose eggs could be successively taken for incubation, to produce chicks for release, following Peter Scott's model (which saw the Hawaiian Goose move from desperately endangered to ubiquitous wildlife park favourite). Theoretically, at least.
According to Wikipedia, the Great Indian Bustard has resisted attempts at captive breeding (also includes the rather Gerald of Walesish snippet that when threatened, hens are said to carry young chicks under the wing), but the programmes in the Middle East (for the Houbara Bustard) successfully use artificial insemination, so the problem isn't in the mechanics.
The history of the Porton Down Great Bustard Captive Breeding Programme is quite a sad one. The last male died in 1999 at Whipsnade Zoo; no chicks were ever produced. It's tempting to think that perhaps the thing they really object to is enclosures, or captivity itself, but that's lazy, anthropomorphic thinking.
With thirteen years of the Smithsonian's successful Kori Bustard breeding programme to draw on, a captive breeding programme might have a better chance of success now. You wouldn't want it instead of the current programme though; it would have to be a supplement. Maybe if they get enough birds that accidentally tame despite the awesome dehumanisation suits, or which turn up injured, they could give it another go. You'd need more than two, though; lekking species don't do couples. Peacocks work quite well on one male, three females -- that's how we used to do it, anyway.