In the scenario you are proposing I think I'd use 2 1/8" flats. One below the floor and the other above. You'll never get a good weld trying to combine those two vastly different thicknesses of metal (14 gauge sheet and 1/4" mild).
The support channel you are replacing is designed to provide lateral support and prevent the seat from becoming a "launch" seat in the event of a catastrophic impact.
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