How would this design fit on a table?
Is it supposed to be free standing on the table or to span between two tables or what?
Have you considered the horizontal and vertical reactions at the supports?
I think they have given you a clue here as you state the max grade is 10%
A simply supported beam has only vertical reactions.
No horizontal abutment reactions or moments.
An arch has no abutment moments but does have both horizontal and vertical abutment reactions.
How are you to fabricate this bridge?
Is it to be made from sheets of cardboard, cut to shape?
Glue? Pin joints?
I know you said you cannot use a suspension design, but can you use string to prestress the beam?
If you want to use a truss, and the above fabrication methods are available I would suggest cutting the cardboard into rectangles and rolling these into longish cylinders and gluing the joins. Also change the truss design so the compression members are much shorter and/or fatter than the tension ones, otherwise the cardboard will buckle.
We can look again at the abutment question when you clarify what the bridge is to stand on, as your current idea will not work well.