What if you went with some canvas for the colder months. Pieces that have snaps around the edges that snap to your bed roof and to your bed sides.
Perhaps even some windows in the middle that have that fly netting on the inside of the window so you can see out. Then even sew on canvas overlap for the window incase you want to close if the rain is coming sideways. Sew at the top of the overlap then have a snap at the bottom to snap it shut and snaps at the top of the window to secure it open.
I don't know if you can find this, but if you had a scissor type of jack on both sides that could lift your roof up and provides fairly sturdy sides.
something like this but no this one.
You're idea is close to a Maggiolina in concept. There's just some simple things you could do to get it close to one and it'll be larger inside for very little cost.
It could work with some modifications for colder seasons.
Or you could get a rack made and get a Maggiolina on the back of your bed.