I'm in a similar situation, I can get a salad at work for a couple bucks so I have a hard time saving money packing lunch. The key for me has been to start bringing food that is "free". Leftovers sometimes get thrown in our house, so bringing leftovers can result in a free lunch. But if I purchase specific foods for lunch I can't really beat the cafeteria price.
I found I couldn't resist the drink, so I stopped trying and keep a diet caffeine free coke in the fridge for lunch. It costs me about 25 cents. Not mustachian, but better, cheaper, and more enjoyable than paying for a drink every couple days in the cafeteria. The deserts still tempt me, but I only splurge about once a month, and I try to make it something I really like, not just because I'm feeling extra vulnerable to the idea of desert that day.
So I think you have a solid plan, but like me you have to make sure you stick to it or it can revert to the mean of cafeteria lunches, which ain't good.