The way I look at it, leaky gut prevents you from absorbing all of the minerals and nutrients you need to get better, so you gotta supplement with vitamins and trace minerals. I haven’t looked any studies about it, but in my opinion, if your gut lacks the surface area and bacteria to properly convert/digest these foods to energy, you likely are not getting everything you need.
I haven’t looked into any multi-mineral supplements really, but solgar makes a calcium/magnesium/zinc combo vitamin that gets 3 of them all in one for you. You then could add in selenium and/or iodine on top of that. There are more minerals you need of course, but these are the major ones. If you take selenium, be sure to take it with vitamin E which will allow for greater absorption.