GAPS is very compatible with Paleo. The "maintenance stage" is basically a grain-free, low sugar, whole foods diet with an emphasis on traditional foods such as ferments and bone broth. If you are already committed to remaining Paleo for life then committing to GAPs for life is very similar, except on GAPS you can eat a few types of cheeses and some legumes. It's your choice whether you do or not of course. GAPS is pretty restrictive about not introducing any preservatives or fake foods, food additives etc. Many people continue to use their herbal remedies in a tea form. Many will continue to use tinctures when ill, especially if they are on the maintenance phase (although it wouldn't be recommended in the first few healing phases of the diet, but of course if you are really ill you do what you need to do).
To more fully answer your question about "GAPS for life" I would say that it's likely you will have to restrict your diet for life because if you go back to a grain-filled SAD, you will probably end up right back where you started with an unhealthy gut. However, after you have healed your gut, you may be able to incorporate a lot more foods into your diet than are usually used in the GAPS protocol and do some type of Paleo/GAPS/Traditional Hybrid depending on what works best for you and your family. For example, you may be able to introduce some rice slowly and carefully or some traditionally prepared beans.
I'm not as familiar with SCD, except that it's more restrictive in the foods you get to eat and it doesn't have all the stages/phases that can be really confusing at first with GAPS. I personally have chosen GAPS as my healing strategy and am happy with the choice.