(I'll assume you don't have a jointer)
I am new to the Grrr-ripper myself, but it is quite obvious it is not to be an all inclusive push block. It is appropriate for some cuts and not for others. This isn't one of them.
I'm not really understanding the complication of this cut, as long as the 2x4's are straight. You definitely want to cut like your first picture, with the waste to the left. If the 2x4's are 8 footers, outfeed support is an absolute must and will give you much better control. A roller stand on the infeed side would help a lot too. Other than that, standard push sticks will do just fine and should allow you to make perfectly safe cuts.
Ernest Hemingway once wrote, "The world is a fine place and worth fighting for." I agree with the second part.