I have long advocated that a gluten free diet or a more severe elimination diet is a worthy trial for any chronic condition. Six weeks should be enough to see improvement on an elimination diet, although it may take considerably longer to completely repair an inflammatory condition.
However... When you eliminate a foods from your diet that are partially digested by bacteria in your gut, you can starve out those bacteria, and when you reach the end of your elimination diet, you might have a completely different gut biome, which is no longer able to digest large classes of carbohydrates.
Wheat is the biggest contributor of gluten to our diet, but it is also a major contributor of fructans. Another important fructan to know about is Inulin, which is a well recognized prebiotic. A prebiotic is a substance that helps keep your gut biome healthy and beneficial to you.
So when you're trying an elimination diet to address a health issue, you might want to make sure you're still getting enough of these prebiotic substances to keep your gut healthy, especially fructans if you're avoiding wheat.
If you have gotten yourself into the trouble that you can no longer digest one of the classes of FODMAPs, you may have a long recovery ahead of you. Infants generally take years to build up the bacteria in their gut to adult proportions, and you know how much dirty stuff they put in their mouth to acquire bacteria. How much longer does it take for a clean living adult? I'm slowly coming around to see some value in the GAPS and Weston A. Price obsessions with probiotic foods, at least for people that have imbalanced gut bacteria as evidenced by favorable response to the low FODMAPs diet, or young children that are still building up their gut biome. The fermented food is pre-digested outside the body, better able to be completely digested inside the body before it causes trouble in the lower gut, and some bacteria may survive the long trip through the gut to take up residence in the large intestine where they are needed. As your gut biome heals, you should be able to slowly increase the amount of FODMAPs you eat without fermenting them first, and feed that fermentation vat in your own gut, slowly changing the proportion of bacteria present. But if you ferment all your food before eating it, are you right back to starving your own fermentation bacteria?
One more little bit about probiotics. Most probiotic foods contain lactobacillus. Lactobacillus is very common in infants, not so much adults. In the adult gut, lactobacillus makes up a small percentage of gut microbes, and is completely absent in many individuals. (I'm lacking data, but I suspect it is absent in the lactose intolerant.) It may be that lactobacillus does help change conditions in the gut to be more friendly for the permanent residents an adult needs, but it isn't going to help you digest all classes of FODMAPs. It may be beneficial to shop for probiotics based on varieties of strains rather than cell counts, and to rotate through several brands/types to find the one that introduces the right bacteria you need into your gut. Once you've seeded the right bacteria, you need to keep feeding them. If they die out you may have to start over with rotating through the types of probiotics again.
There is still a lot of speculation and unknown variables in the science of gut microbes, but perhaps I've given you some leads to research further in your own quest for health...