I have various food allergies and eat essentially vegan. Can tolerate small amounts of dairy cheese and dairy butter but do much better without it (have dairy and egg allergies). Finally just bit the bullet and buy good vegan equivalents to keep me away from dairy entirely ...
I don't have ibs but my innards have never worked quite right, so ibs advice can help me. Heather's enteric-coated softgels with peppermint, fennel, ginger oils have done wonders for keeping my GI tract calm, but contrary to the usual instructions I have to take them after starting a problematic meal (along with vegan chewable enzymes works well). Simple meals such as fruit with nuts/seeds/peanuts or their butters are non-problematic for me. Peanuts in any form have always been very safe for me.
Interesting that your list seems to include beans/legumes that are known to be low gas producers. I don't have my list handy (dead battery on that phone...) but grains like rice, millet are on it and the low-gas beans include Fordhook Lima beans (better than baby limas actually), certain lentils, and chickpeas (garbanzo beans). Most non-starchy veg are often ok. Can't remember about fruit but it doesn't cause me trouble in the amounts I eat (I freeze fruit, sliced if needed, and so might naturally be eating smaller amounts than most people). Although with beans, they tend to cause less trouble if you eat them more regularly, starting with small amounts you know you can tolerate. I freeze rinsed canned beans in my own preferred portion sizes, which grew over time.
I found lists of low gas producers by keyword searching. I think I used low gas foods as the keywords. Maybe Heather has such lists also. I don't really seriously cook so I haven't looked closely at her suggestions for meals etc. When I'm having trouble, small meals with few ingredients (even just one or two foods at a time) help me. That's the approach I used during the initial diagnosis/control phase of dealing with multiple food allergies. It can be helpful for anybody trying to track down which foods cause trouble and which don't, regardless of the source of the problem.
I also found it helpful to rotate foods according to food families and just eat a variety rather than the same thing all the time. I would just hit my basic food groups over a day in multiple meals: nuts, seeds, veg, fruit, grains, legumes, miscellaneous like nutritional yeast and mushrooms. I revert to that when under a lot of stress. Really helps to have developed a solid list of foods that never cause me any problems.
I can eat rice of any type (white or brown etc.) in any form any time (even under stress) with no problem, but something in wheat (not apparently the gluten) bothers me so I have to avoid that for most meals. Certain commercial wheat breads are easy on me, such as whole wheat pita breads and Dave's Killer breads (such as the 21 Grains & Seeds one), don't know why. (My homemade bread causes more problems.) I tried checking for FODMAP problems but didn't really seem to have that problem at least with my eating patterns.
Anyway, humans are not obligate carnivores so a vegan diet is fine for us. Even just eating vegan a lot of the time can be helpful to people with the carnivore habit and can help discover which animal foods are problematic for them personally. I've often heard people say even just cutting out red meat can help with some chronic problems, but don't know why.