I don't know a lot about celiac, but it sounds like a paleo style diet might help you. Your eating meat, veggies, fruits & dairy ... basically whole foods.
I know gluten free things are expensive, but have you thought of using corn tortillas. They are gluten free already & one site it said to check the packaging for possible cross-contamination. A lot of brands do put allergin warnings on things now.
I felt better when I did paleo. Once I cut the bread out of my diet, which was hard at first, I found out I didn't really miss it after all. I used lettuce leaves as wraps for tacos, sandwiches & things like that. I also found low carb wraps (still had flour) to use. What was the hardest thing was losing my desserts. I found some low-carb/no-carb recipes for desserts which were okay. I did have cheat days once in a while for real desserts, but I didn't overdo them when I did & still statisfied by sweet tooth.
I've been leaning more towards a paleo-style diet again. But I am still eating steel-cut oats & potatoes letting them sit for 24-hours to change the starch into a resistant starch.
You may need to do a little cooking to cut back on the grocery price, but it's not difficult.