the strips on the bottom do help in keeping that section of the rubber from getting trashed quickly, it tends to sag and get mangled - the screw holes may have been filled sometime, they should be there, right along the slight ridge the rubber sits on -
an original [after chem strip and sitting for years

] - it just jams against the rubber where there's a slight sholder it sits on, keeps it from getting stuck against the step when cold and wet and getting pulled every time the door is used
if the weatherstrip is the right stuff [Steele, from many vendors] it has the pegs that go in the holes and has corners molded, so the piece should only be able to go on one way -
the higher lip toward the opening - note little clips at the bend also, they're factory
the closing problem is prolly adjustment, maybe need a wider gap at the front, less at back, and maybe they need to be adjusted slightly outward .... the TF doors are definitely a bear to get right, I'd bet the assembly line guys cussed'em all day long
Bill