Can I selectively breed my sourdough starter?
Yes, but it might have other effects that make it less effective as a leaven. 

When I was experimenting with sourdough in the past year or so after a long hiatus, I had a pretty good batch going and parked half in the fridge, then had some life events that caused the part that was out to be left 24 or more, not 12 hours between feedings, and it turned very, very sour - but it also didn't do much for raising the bread.

Unless you are fixated on getting there via sourdough, I'd suggest picking up some citric acid if you like your bread "as sour as possible" - though even that might do in your yeast if you use too much - of course, there's always really sour flatbread, I suppose, by either method.