The obvious solution is to eat cooked vegetables instead. When foods are raw they are very tough to break down... and cruciferous vegetables (like broccoli) and legumes (like peas) contain compounds that cause a lot of gas .... think what a pan of boiling cabbage smells like and how much beans make you fart
So maybe keep the carrots, cut thinly and chewed well, but choose a more easily digested selection of raw foods e.g. cucumber, cherry tomatoes, celery. Cook things like broccoli, cauliflower and peas... And only eat your raw foods with a meal rather than introducing them to a completely empty stomach.