High five for making the decision to do this. You'll be so glad you did when the relatives in your generation start getting diabetes, etc., and you don't. Phasing sugar out might work just fine for some people, but you just said it doesn't work for you:
One of the problems is - when I think "Well, I'll start as soon as I've cleared out the pantry", I start binging on eating all the fudge/chocolate in the house, because hey - the faster I get rid of it, the sooner I can start right? But let me just first finish off all that left-over rice in the fridge before I start. Oh, and I can't start today, I still have a box of cereal.....
So yes, cold turkey. If your motivation wavers, imagine if an alcoholic said, "I'll stop drinking as soon as I've finished drinking all the liquor I already have"! Would that sound like a workable plan?! Haha, no way!
What's a good substitute for snacks - fruit? (Though even fruit can be high sugar, I don't want to replace one with the other) Muesli/nut bars are expensive unless I make my own. I'm going to get very tired of eggs, very quickly....
- Fruit; sliced apples with peanut butter are a tasty snack. Of course I mean NO SUGAR peanut butter--just get the real stuff, ground-up peanuts with some salt and nothing else added. Sliced apples are also good with a bunch of different kinds of cheese--depending on the type of apple, I tend to prefer Swiss. Perhaps you are sensing a theme here: yes, it's fruit AND a protein-fat combo. That will make you feel much fuller and keep your blood sugar on a more even keel.
- Veggies (carrots, peppers, whatever you like). Again, some of them are good with a protein-fat combo: carrots go well with peanut butter, for instance.
- Nuts. Salted, unsalted, roasted, not roasted, mixed, not mixed... they're great for you and they fill you up pretty well.
- Nuts mixed with something, a la raisins. Beware of dried cranberries--they almost always have a bunch of added sugar.
- Eggs, like you said.
- Avocados, if you like them. I absolutely love them. Sometimes I bring one to work, cut it open and just eat it with a dash of salt. I eat it with a spoon right out of the skin after cutting it in half. The trick to getting the pit out is a sharp knife: press the point of the knife against the pit, slam the avocado half against the counter so the knife goes into the pit, and then you can pretty easily pull the avocado half off the pit.
- Jerky-type meat. Also, if you have a fridge at work, you can bring other kinds of meat--canned sardines or salmon, microwavable hot dogs, etc.