Has any one tried to take a piece of plastic type screening and cut it out and
form it into a "pocket" so that it slips over the top of the door frame?
Something like this, maybe :

                            # ###########################
                             #                                             #
                        ----> #                                           #
                        |       #                                           #
<----|
                        |         #                                         #
| join seams
  join seams      |          #                                        #
|----------------------
  -----------------------          #-------o-------------------o----------#
|
  sew or hot glue|          #         fold here                   #       |
                        |          #
#<------
                         ------>  #                                         #
                                  #                                          #
                                 #                                           #
                                ###########################

           fold over to form pocket, join side seams by sewing or maybe hot
glue gun.
Leave bottom open, slip over top of door frame, and presto--screen for front
doors...
Maybe!   You could even leave it in place while driving......