I recently went on a 3 day backpacking trip at Dolly Sods Wilderness area in West Virginia. Campfires are allowed in existing rings, so I did not carry a stove. I had the same concern about missing my fresh veggies, so I took a few with me.
The fresh food was worth it, including:
frozen sirloin steak for first night, packed in an insulated bag with some frozen water bottles
foil wrapped sweet potatoes (first and second night, cooked right in coals)
1 small jicama
some green tea bags
an orange or 2
For the remaining meals, I went with non-cook stuff, including:
dried fruits, including blueberries, mangos, bananas
canned kippered herring
Artisana macadamia / cashew nut butter packet
My biggest problem was in judging portions. I ate most of the fresh food, but I took at least half of the dried food.
The only foraging I did was for wild blueberries.