I'm just spit ballin' here. It seems to me what might work is a trench fire of sorts, burnt down to a good bedd of coals. a grill suspended over the coals, a tripod of poles around all that, finally wrapped with a welding blanket (tee-pee style). A little smoke wood and you're good to go.
The grate could be fashioned on site from green wood branches (should be in scout manual) and all you have to pack in would be the blanket and maybe some cordage. Even that could be foregone if the tripod (or more poles if necessary) were shroulded with thick vegetation as would be done with temporary emergency shelter (again should be in manual). Think thatched roof.
Unfortunately the cheaper you go, the more work it is. You could possibly do it with a very large cardboard box, that you could burn afterwards, but you still have to pack it in.
Maybe you can expand on some of my ideas and come up with something that works for you. Let us know what you come up with.