Lily - you can DEFINITELY eat natural PB on SBD! I think it is even a phase 1 food. All nuts are allowed, he just limits the quantity because of calories. Also if you have the original book there have been changes to the diet since then. On the SBD (pay) site the diet now includes milk in phase 1 and 2.
This is my overall feeling on SBD...For one I think it saved my life because it got me over insulin resistance and it taught me a whole new way to look at food and meal planning. I no longer think of the starch first or second in a meal...it is kind of an afterthought. And when I do think about starches I prefer the ezekiel breads and the whole grain stuff.
I think that phase 1, as unbalanced as it is, is important just as what it is meant for, an induction and kind of a mini cleansing ...because when you have gotten rid of all fruit and starch for 2 weeks then you feel so free when you get to add limited amounts back in.
However I do not follow SBD NOW. I followed it long enough to where it became second nature to reach for the lower glycemic items first over the higher glycemic items. But I guess you would say I am in Phase 3 where there is NO food off limit, just realizing that some foods may affect your blood sugar more and they should be limited. Plus I dont believe in artificial sweeteners so I always was different there. Since your weight is in maintenance, I would think that you could progress fairly quickly. I would give Phase 2 enough time that it seems normal to eat that way and combine it with calorie counting (I HAD to calorie count with SBD, I didnt lose weight with just SBD) and then you can strategically add in the stuff you love. You may be surprised at how much less you crave though.
I would say that my diet is 80% SBD and 20% whatever.

And I was so good yesterday! I had oatmeal for breakfast, some light weight Progresso soup for lunch, carrots and grapes for a snack. Angie was still at our sister in law's for dinner so I made hot dogs. I used the Hebrew National 50 cal ones. I had 2 on whole wheat tortillas with a piece of cheese....and 1 without anything, stayed away from any kind of chips and had a little cantaloupe. Oh well...that's life! 
sad that we HAVE to remember that day.
Good luck with the new menu.