When you say "veggies" what do you mean?
I ask because "veggies" to me means broccoli, raw and slightly cooked peppers, raw and cooked carrots, etc. "Normal" veg. I don't particular like these either. I definitely don't like them raw!
I'm figuring out that my tummy isn't comfy with raw veggies. However, I really, really like cauliflower if it's made into a mashed-potato-like mash, roasted peppers if the skin is peeled, "odd" veggies like brussel sprouts and kohlrabi and eggplant - if I put a "sauce" over them, etc.
Your #1, 2, and 3 vices sound like mine so I'm interested to see what other people have to say!