Background: This system presumes that my theory is completely correct (I do). Artificial selection is all well and good and has a proven record of succeeding in breeding stock with desired characteristics. However, the characteristic in question must exist in the population to start with. This is highly unsatisfactory and there is just no way you could, say, breed an antelope with a considerably longer neck (or taller all round, like a giraffe) without triggering appropriate mutations first.
The trick would be to find the same stress/mutation trigger that caused (say for the giraffe) those mutations required to be more prevalent, which allowed natural selection to have something useful to select from and speciate a taller (long-neck) animal.
The first condition is to pick an animal that feeds on leaves. There is not much point picking a carnivore or a herbivore that only eats grass/fruit etc. because there is no natural situation in geologic history in which a long neck would be the difference between life and death for such. I choose the antelope in this case - it eats leaves and lives in the same continent, so might share the required triggers and responsive genetics.
The second condition is that the breeding stock must be in some kind of stress. This is considered animal cruelty, so I suggest any experiments are done in a subsaharan country that is in a state of war: Nobody notices any cruelty that happens in those countries. Stress is well known to trigger mutations and is highly necessary to accelerate the process of artificial selection.
The third condition is to pick a stressful situation appropriately. Adaptive mutations happen as a mutation response that succeeded in the geologic past. They may not be apparent in the animal because they eventually reversed in the normal cycle of things - hopefully numerous times in the species' history such that it reinforces the response(s). In the case of the antelope, the stressful situation might have these features:
1) Near-starvation. This is known to also have physiological responses of delaying maturity, among other things. It is likely to trigger responses that might achieve it more food for its progeny in analogous situation.
2) Declining and/or isolated population. This reinforces that it is likely to be a long term stress, and which migration is unlikely to resolve. Inbreeding and polygamy might be physiological indicators of this.
3) Visual cues that food is plentiful higher up. Perhaps just out of reach, or even selective cues like seeing that taller relatives are better fed.
4) A lack of predators. Predators are known to put selective pressure towards earlier maturity thus smaller form.
I don't know if penning up antelopes, while at the same time putting heaps of food just out of reach of all but the tallest is an ethical way to prove Lamarck right - But I think that is exactly the sort of thing that led to Giraffe's long necks, and could be demonstrated within the space of a few lifetimes.