K2's advice is what you should be following, as it is the whole gist of Heather's program. Your sample diet seemed shocking to me when I first read it because it sounded like more IF than could be handled by most at least at first, especially the salads or the veggies with no sf to cushion them. It depends on if you are c or d, but I would think that if you wanted to keep a similar diet (minus the meat and cheese triggers), you could try eating just a bit of what you already are but matching it up with some sf like rice or pasta or white bread/bagel. I'm a d and I'm just learning, but the sf has definitely started to help give me some formed/bulkier BMs anyway.
-------------------- Originally IBS-D for a million years!
Then IBS-A, Now a transformed slightly C