The experiment would be constrained in that you can only test 1152 reactions (3x384). You can put more than one protein in a well, but you need to come up with the most cost-effective way to identify the protein that interacts.
The O.P. is a tricky question, because it says that a sip is lethal after about 24 hours. This does not mean that you can do a single experiment in those 24 hours, because toxicity is in the dose. You could give the rabbits a higher dose and see a result quicker, but I am not sure how the rabbits would react to a higher dose of alcohol. That might be lethal to them as well.