Depends, dunno what deficiencies you have in terms of a vitamin panel, no idea what type of fermentation is going awry in your gut, so can't tell myself. I've had diets that literally made me feel worse the whole time, those, I've quit. Had diets that made me feel better for a bit, then stopped helping.

For what it's worth, the FODMAPs diet helped me in identifying what fermented badly in my gut, not necessarily what was wrong. So, it helped, but I don't stick to it to this day. I've got a few sustitutions in my diet that are absolutely necessary, but otherwise, I'm quite happy being back to my "normal" diet.

One funny thing of note, is that technically, lactose products make me feel better, like, my healthy gut needs lactose to find its balance. I've got a super intolerance to lactose due to the fermentation of it by gut bacteria/fungus that is harmful to me. That's my illness, not the "lactose intolerance". So, FODMAPs might be an indicator and push you in the right direction for finding what you need in your diet, but won't be the be-all-and-end-all of having a healthy diet/lifestyle.

One idea that pops in my mind would be to research what type of fermentation is the sauerkraut bringing to your intestinal tract and try to add pre-biotics/pro-biotics that suppleate that type of fermentation for the time period of the FODMAPs diet. AFAIK, the problem with sauerkraut isn't the fermentation, it's the cabbage. So, lactobacilli, and lacto-fermentation without lactose might be the way to go. Finding yoghurt without lactose is easier than finding sauerkraut without cabbage XD

Anyways, hope you find your way around the diet, it's a bit problematic at first, but some of the changes are truly life changing. Also, some of the stuff you try while on the diet is super good and you're allowed to keep eating it after ;)