Always to be 100% honest, I simply can NOT see a likely scenario in which this huge delta in demand vs. production will change anytime soon, when it comes to Patek (and also for select few other brands, though often for different reasons). If you're interested in a given Patek, however, be it the 5711/1A or any other reference, it certainly won't hurt to show an interest to one or two ADs -- this is the best you (or anyone else) can do, and sometimes we get lucky! ;-)
Cheers.