I can't answer your question.
I can say that it is not likely the total weight, but more the weight being concentrated in a rather small area.
Off the top of my head, a piece of aluminum diamond plate cut to fit the floor area will definitely distribute the weight without adding much weight. The material is fairly expensive though. There may be other ways to distribute the weight which would be less expensive.
A couple low profile Unistrut or Superstrut rails for the batteries to rest upon may also work.
Shop SUPERSTRUT 1-5/8-in x 13/16-in Gold-Galvanized Half Slot Channel Strut at Lowes.com
My vision would be for the additional supports to rest on the existing floor structure, not attached to the underside.