I have a flexi 2001. Space isn't an issue.
when not in use I store the wheels under a bed, I leave the frame complete, although I fold the seat completely forward (takes 1 sec).
I store the frame upright (only about 8 inches wide at widest point) in hall cupboard.
When transporting, it goes on it's side in the footwell of the back seat, can still fit one passenger in back seat like this ....
no problems...