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Personally, I wouldn't run my floor boards across. That gives very little strength. 20" wood is not cheap, but it is available.
It looks like a frame to axle mount reinforcement could go along the c channel and a couple feet beyond. I'd use a flat, maybe 8" wide and 5/16 thick.
How far is...
The area that your springs mount could use some reinforcement and some X bracing in the frame would help. If your floor is steel, like diamond plate, welding it on will give a lot of strength. If using boards on the floor, full length would help (and be pricey at 20').