I also say go the gradual route if that it what makes it easier for everyone. That's what got me on the road to gaps. We are far from there yet, but I picked up the gaps guide a few months ago and it said:
"go buy some coconut oil, and keep eating the way you are suppose to be eating. Now research where to find some good bones, buy some and put them in your freezer, and keep eating the way you are eating. Now take the bones you bought out of the freezer and make a broth. try, it. kinda bland huh? keep eating the way you are eating. Now put some veggies in the broth. tastes, better doesn't it? keep eating the way you are suppose to be eating."
when I read that I realized that was something I could do, take babysteps until I can get there. So slowly I add new things while taking away other things while doing more research and learning as I go along.
I attempted to rid us of all grains and then realized we didn't have the $$$$ to fill in the gap (no pun intended) with other foods and the kids were HUNGRY! So for now, they still eat grains. I cheat now and then but for the most part I am at least trying to keep myself in the paleo on my way to gaps mindset. But we have a waaaaaay smaller grocery budget even then you have so we just do what we can. I know what my ideals are, and then I know what my reality is and that is that these diets cost $$$$$$.... so until I can afford to go all out, it's baby steps and more baby steps. Don't feel bad if you can't jump in and go all out right away. Allow yourself to get there when you can