John took the correct approach to solving this.  I don't have the data on the beam handy to find the area moment of inertia, so I can't verify his numbers.

The deflection calculation goes as defl=load*span^3*/48/E/I   The 48 number changes depending on how the beam is supported, this is for a simply supported beam (not clamped at either end, or cantalivered).  You can control 2 number in this equation, span and I (area moment of inertia).  Welding on another plate to the bottom of the beam would be massively helpful...but not cheap.

Since the span length is a cubed fuction, if you can halve the span, the deflection (and stress) will go down by a factor of 8.  Buying more load cells is probably the cheapest solution.

You will have serious problems if anyone drives a wheel down the center of the scale.  I would elevate the entire scale off of the ground to ensure that if the truck is on the scale, it is properly centered.