I think it will just make the flexing move to a different area. I think just getting one 83" 4" wide 1/4" thick piece of flat bar welded onto the backside should do it.
That likely works if you are a little overloaded or your frame is weakened. (Depending on how overloaded you run)
Remember that up to 90% of your loads are were the axle/springs mount to the frame, the further away the less load
I personally don’t like edge welding because of potential rust and cracks down the road but it depends on the quality of your rails and if you run through winter salt
A boxed frame is indeed much stronger to loads along the length of the trailer but still can end up a parallelogram if your running way overloaded/ unbalanced/ off road.
Also remember your frame needs to bend to stay strong, so long as you aren’t way off base it “may” be ok or may be catestrophic
On HD dump trailers a suspension crossmember similar to what is shown is used , however it’s normally 4 separate pieces of C-Channel
2 in the rail covering and bolting too the suspension mounting points with 2 c-channels twinned in the middle cut to length, hammered in and bolted on the flanges to the outer c-channels
The hd stuff uses lots of grade 8/9 bolts to hold everything firm
Only you know how overloaded your running, The design of your trailer may not allow a crossmember in which case you gotta box
Itend to build things like a tank but I doubt your running 5 ton of gravel on a light duty trailer :0
What I find more amusing is how underbuilt some trailers are compared to others of the same load rating.
Sometimes gotta fix design errors, similar to the crappy trailer hitch ratings that don’t allow for real world occurrences like a flat tire.