If I'm doing my measurements correctly, Berliner is basically the same width as a 50-inch web broadsheet - about 12.5 inches - and is about 3.75 inches shorter than the broadsheet, right? 12.5" x 18.5"? I'm just trying to picture the size. I'm also curious why they had to get new presses - granted, I'm very naive about how presses work, but why can't they be reconfigured to cut the pages shorter?

I believe it's 12x18.5. That's what the Lafayette Journal and Courier in Indiana is.

When do they move to Berliner, or have they already?

The 'Berliner' size is (metric, I'm afraid) 470mm x 315mm or roughly 18.8" x 12.6" according to Man-Roland who are the makers of the £50m presses being installed in East London . The new presses were necessary because 'Berliner' is not a convenient multiple of current British newspaper sizes (the conventional UK tabloid is half the conventional UK broadsheet). The 'Berliner' paper size is more like 2/3 of a broadsheet.