Here is a link to an excellent article on packing PAB cups, comparing methods for packing small and large cups. Following this method for packing, I was able to get 331 1x4 bricks into a large cup. So assuming this method gives you near the maximum amount of bricks in a cup (I can't imagine any method doing too much better), you will need at least 2 cups. But with 2 large cups, you will easily fill your entire wish list.
LEGO® Pick-a-Brick Cost Comparison Analysis
Yes, you are correct, but I was speaking in general terms. I am now 'eagerly awaiting' what the PAM selection will be in April 2016. Sometime around the early part of March, the April calendar will be posted and we will get our first look at the new PAM models. Then you can try to deduce which parts will be included with that model. And I will start planning how I can maximize the number of desirable parts in my PAB cups.