I think your plan sounds good. That's kinda what I did. I went somewhat slow...but I did make a plan, as before the plan I was wishy washy and it seemed like I kept making excuses to eat this and that. I made a 3 week plan. 1st week no more grocery shopping of non-vegan. 2nd week no more snack/cafe purchases, 3rd week no more restaurant purchases of non-vegan food.
Someone here gave me good advice which really helped me into my adventures into veganism, so I'm passing it along. Don't think of non-vegan food as food...if you think of them in terms of stuff you would never eat such as cockroaches or pig's milk or disgusting stuff like that you can get over them faster. It's the way we look at food. For example we'd never climb a tree and take a robin's eggs out of her nest and make an omelet with it, but we have no problem doing that with a hen's eggs. We wouldn't think of milking our dog for our cereal, but yet cows are okay. That really made me get over eating anything that had animal by-product! In fact, I was a cheeseaholic too and my fav. was brie! I still have a whole wheel of it in the fridge...and although I have stopped buying anything non-vegan I was still going to go eat what I have in the house. However, that I can't make myself eat....it's just too much. The whole idea of eating that makes me sick to my stomach.
I also agree about not substituting, as it's usually disappointing because it won't taste the same...such as soyogurt: yuck! However, find new products, such as soy pudding: Yum!!!