How Easy Is It to Switch from Your Average American Diet...

to a sort of Paleo-light while having to shop on a budget?

Carbs seem to be my weight-loss's main enemy. When I start eating a decent amount of carbs again, my weight loss stalls. While I don't want to cut them out entirely, I would like them to become a sort of rare treat rather than a common thing. While I'm not willing to give up milk or cheese, I'm interested in switching over to a Paleo diet... but I'm worried such a protein-heavy and produce-heavy diet will break our grocery budget.

What is your advice on the switch? What are the cheapest Paleo-approved foods I can buy? I'm planning to switch over my breakfasts from oatmeal to eggs, bacon, that sort of thing and I try to plan for lunches where I can make a whole ten servings in advance to get my husband and I through our work-week. Dinner is usually heavily based on what vegetables and fruits we receive in our produce-delivery service (local, organic stuff).

Advice? How can I effect this switch and stay within our budget?

Our every-single-week-buys:
Milk
Cheese
Greek yogurt
Black beans
Spinach
Eggs
Tomatoes
Chickpeas
Bananas
Apples

We try to always keep tortilla chips and salsa on hand for snacking, but I'm phasing that out to replace with nuts to eat with the fruit we're buying anyway.