The Specific Carb diet seems to closely resemble the Paleo diet. I've closely followed the Paleo diet and it has helped my GERD a lot. I have been off PPI's for about
4 months now and am taking 1 pepsid and tums as needed, right now 2-6 a day but slowly decreasing the amount. I have been able to eat some grain based items without it affecting me as much anymore but limit this to 2-3 times a week. My normal eating habits consist of fresh fruits and vegetables and fresh meats. I no longer eat any canned foods or processed foods. I prepare everything from scratch and now eat fish 2-3 times a week. Prior to this I would eat a lot of pasta meals and almost everything was processed. The pantry used to be stocked full of canned food items but now is just a storage area for the most part. The fridge is also now usually full with fresh foods where before it only held left overs. As you may know, results may vary between people, I think it would be a good route to take if you are able to keep with it. Certainly wouldn't hurt. I went from having heartburn 2-3 times a day while on 40mg Protonix a day to hardly any heartburn on 1 pepsid OTC and 2-6 tums a day. It does take the body some time to heal but it's worth it if you are able to stick it out. If I keep moving at the pace I am at, I should be completely off any form of medications before the end of the year.
I was also on PPI's for about 8 years and had a lot of rebound coming off them. Your results may be less dramatic as mine since I've found that the rebound effects are different for each person and if you have rebound, it may not be as intense.