Honestly, I'm not sure that once every few weeks is a reasonable expectation.
Especially when you're talking about staples like grains.
I can make huge variances of what we serve over the grains, but switching out the basic grains itself so many times is hard to do inexpensively. That leaves the option of the meat being the primary substance which is great, but adds $$$.
Variation is most definitely possible. Meal planning on a limited budget is most definitely possible. I'm not convinced that you can accomplish both completely simultaneously.
Is he fully on board with the budget cut? I think I'd have a discussion with him to see what's the bigger priority -- budget or variation.