Hi Flaky - I was also one of the unlucky folks - I didn't gain weight whilst b/f, but i certainly couldn't lose any. My H/V said that some womens' hormones make then sort of "grab" all the calories going in order to safeguard the baby's nutrition.
Your plan may well kick-start things - no alcohol is always a weight-loss winner, as alcohol is "empty calories" (didn't know what that was till I Googled it - too lengthy to go into here, have a look).
Not sure about the dairy thing, mainly due to my love of all things dairy.
The wheat - now there's a subject. I have lost a serious amount of weight (in excess of 70 lbs in a year) by eating low GI. The worst offender is wheat, ie bread, pasta, pastry, biscuits. Also potatoes, rice, polenta etc are on the no-no list. I can have lentils, butternut squash, sweet potatoes and chick peas, including hummous, also those Ryvitas with oats and sunflower seeds/pumpkin seeds.
This might sound like a miserable existence, depending on how much you like carbs, but I eat all the stuff I like and still lose weight - meat, ham etc, cheeses, butter, yogurt, mayo, bacon, eggs, veggies, fruit, salad, salsa, hummous, dressing, olives, anchovies, drippy stuff in olive oil. In extremis, I do eat lasagne, as the ratio of pasta to other stuff is quite low. I resist the garlic bread with difficulty .
A great diet if it works for you, but c**p if you love pizza (I really hate pizza). Whatever you do, check in with your GP, and the best of luck to you.