If you need to shop fortnightly, can you adjust the timing so that the first week is when DSS are not there, the second week is when they are there, so at least they won't be able to help themselves to stuff that's been planned for meals?
Is there any way of labelling the meat "Tuesday's dinner" etc, then freeze? Or label anything available for lunches/ breakfasts , so they all know exactly what they can and can't tuck into for brerakfast/lunch/snack?
Can DH and DSS all be told to plan a dinner with x budget? And what food budget contribution does working DSS make?
TBH if a 16yo has issues that mean that he won't eat the range of foods you've outlined, he could cook for himself. I became veggie at 14 and cooked for myself thereafter, had to meal plan within budget.
If they won't eat potatoes, can you make the normal meal with a portion of meat and veg each, and if they don't want potatoes they can eat cheap bread to fill them up (or they could make their own bread). Or you could make whatever you're having plus a bowl of plain pasta and they can fill up on that if that's what they like.
If they'll eat salad/ peppers/ onions between them could you try stuffed pitta breads as an alternative to wraps? You could cook whatever meat is on special offer that week- maybe slow roast cheaper cuts? I sometimes do slow roast pork belly as a roast dinner for our family, that's usually reasonably priced as meat goes- plenty of yorkshires to fill up on as well.
If they'll eat rice- risotto or paella? Both can be made with veg so no meat needed.
Tapas style dinner- grilled ciabatta bread, some parma ham, roast veg, Spanish omelette, garlic mushrooms, patatas bravas.
Curry - plenty of poppadoms, naan or chapatis, rice, some tandoori style chicken would be relatively dry, plus whatever curry the rest of you like.
HFW has a recipe for quite a versatile flatbread that you could dish up alongside grilled meat and mix-and-match salad.
Hot dogs/ burgers - plenty of buns to fill up on, plus salad/ corn on the cob/ coleslaw.