You can reinforce
If there is no tank immediately below the spongy area (or if there is a gap between the tanks in that area), you can reinforce the underside. What year is your trailer? If it is fairly recent, it probably has pink fiberglass insulation underneath the floor, covered by a thick shiny black vinyl sheet. If there is no insulation, the project is a lot easier.
Anyway, cut the vinyl carefully and remove the pink stuff. You may have to put in new pink stuff if the existing fiberglass is glued down. You will also have to glue a vinyl patch where you cut the black cover -- use a good vinyl glue.
To reinforce, I would run a piece of angled perforated steel across the bottom. Drill into the steel cross beams and use short self-tapping sheet metal screws. If the brace does not put enough upward pressure on the floor, you could shim the top of the brace with a piece of marine plywood.
Once the bracing is in, replace the fiberglass and the vinyl cover.
If this sounds like a lot of work, it is. (I did something similar on my old T-139.) One more thing -- when drilling up into a metal beam while laying on your back on the driveway, be sure to wear a full plexiglass face shield. Ordinary safety glasses may not provide enough eye protection against the metal fragments.