I'm not an expert or anything, but I've certainly done this a few times, and I think there are a few things going on that you could address.
1) Every time I sharply reduce my calories, I am starving for the first few days. For some people this lasts a bit longer. But here's the thing: You're training your stomach, your energy level, and your mind to function just as well (or better, if you're increasing physical activity) on less. So of course you are hungry. But you are not literally starving to death, and if you can follow your plan for a week, it will get easier. Hunger is not an emergency, and a little discomfort now is much better than, say, a stroke in 20 years. Just hang in there. I don't want to sound like I think it's easy, but you have to do it.
2) Yes, eat a lot of low-calorie high-fiber food, but also include more filling things. I try to work black beans and sweet potatoes into my meals regularly, because they feel "heavy" in my stomach for longer than a huge cucumber and tomato salad could.
3) Experiment and see what works. For me, dividing my calories into a ton of small meals means I am never really satisfied, so I eat a very small breakfast (either a packet of oatmeal or an apple with a tablespoon of honey) and a bigger lunch and dinner. That leaves me more full when I am tired and frustrated from work and my will-power is lower, and it means if I suddenly decide to go to happy hour I have some flexibility left. One thing about 3fc, though, is that I've learned that everyone feels different ways about how to plan their food for the day. Keep tweaking, and find out what works for you.
4) Eat hot things. Soup for meals, tea between. It'll make you feel full.
5) Get through a week or whatever of sticking to your plan, and you'll adjust. And it will still be a challenge. So re-read your original post and remind yourself that you don't want to have to re-train yourself. It'll help you stick with it.
6) Whatever happens, hang in there and congratulations on your efforts to get healthy!
Jared, there are slow-burning carbs. Stick to legumes and non-starchy veggies. Whole grain breads and rice, of course, are slower burning than white breads and rice; however, if you have a carb sensitivity, it's possible they can trigger your hunger too. I try to avoid them, except on cheat day. Fruits WITH skins can also be slower burning, but again, they are faster burning than veggies and they have sugar to boot, which is a trigger for me. I save them for cheat day also. I don't know how strict of a vegetarian you are and if you eat eggs and cottage cheese, but those are allowed as I mentioned before, while other dairy is not, except on cheat day. Nuts are good in moderation. I don't know about soy products. The great thing about cheat day is that it helps me to not think in terms of all or nothing, which I have always done. I can have those foods, just not everyday, and I have a much better grip on my hunger now. The diet I am following is called the Slow Carb Diet. You can google it. It was the diet in the book The 4-Hour Body by Tim Ferriss. It's pretty simple, and I make slight adjustments that work for me. For example, I drink water, but I also drink Diet Dr. Pepper, and I'm not willing to give that up, unless I find later that it's no longer working and I absolutely have to. I've read that some people do well with sweet potatoes, etc. That's kind of what everyone has to do--figure out what works best for them, no matter which diet they choose. This diet may not work for you, but then again, it may. You'll figure it out. It will just take a little experimenting. Again, good luck!
Everyone's different, but my first thought reading your post was that more fat & protein would help. Greek yogurt is high in protein and filling. Your diet sounds v low in fat, so 2% or higher could help you out there.
You mentioned eating carrots and an apple for a snack. That wouldn't hold me over either. Have you tried an apple with a serving of nuts? A carrot with some avocado?
Btw, congrats on taking this step! Your plan sounds really good. I think it's likely that if you always pair your carbs with healthy fats and proteins, you'll feel much better.