I'd also politely suggest you're having some blood sugar control issues which could be influencing your hunger.
Your 2-hour postprandial readings should ideally be about the same as your pre-meal ones but all of your postprandials are significantly higher. This isn't medical advice but on the face of it, it looks like either you aren't producing enough insulin or what you are producing just isn't getting used properly. Either way, this means that the energy in your food isn't actually getting into your cells - it's just sitting in your bloodstream. There are also a whole bunch of very complex hormonal interactions between your blood sugar level, your hypothalamus and your beta cells which can also drive hunger when your body misinterprets what high blood sugar means. There's no real need to go into these now as I think the essential point for you is to get your blood sugars under control.
Happily, this should also help with with your hunger quite considerably. As a T2, you have a bit more flexibility in reducing your carb intake safely. Reducing your carbs will reduce the pressure put on your insulin response, giving you more normal BGs. But you'll also have to make up the calorie deficit. This can include eating more protein but you don't want to overdo this as this can cause kidney issues, so the real place you need to pick up on are good fats - providing you are metabolising these, you should avoid any supposedly fat-related health issues. Fat also directly influences satiety and because it doesn't cause peaks and troughs in your insulin response and provides a more steady calorie release, it could also mean you feel fuller for longer.
Put it this way, if I have two slices of toast for breakfast, I'm hungry in about three hours' time. Give me a decent omelette and I can actually go until teatime without feeling hungry.