I have a so many food allergies it's simpler to list what I can eat, not what I cannot eat. In essence, I am surviving on a dozen foods, and I wish I could eat potatoes like you, since I like potatoes so much; but unfortunately my allergies pretty much dictate my diet and rule my life.
One thing though--probiotics are not necessarily the same as dairy products. You can use fermented veggies, like raw organic sauerkraut--standard supermarket sauerkraut is worthless in this respect--or fermented red beet juice to provide probiotics. OR you can get probiotics from sups--lots of those can be found on the net.
The problem is that most of the people who have leaky gut at curezone seem to indicate that they do not tolerate probiotics well, under any form, dairy or fermented foods; they get allergic reactions from them. So try fermented veggies and see how you react;
some people with leaky gut seem to get good results with S. Boulardii sups, like Florastor or the likes. Do a search on this forum with the keywords Boulardii and Florastor to learn more.