Use a screw that will penetrate no deeper than 1 inch into the floor and you should be fine. I have never had an issue and no one I know has either. The floor material is likely no thicker than 1/2", so a fastener that penetrates the floor more than 3/4" is of no additional help.
As a tip - if your tray goes from door to door (96" I think it is), then quite possibly, on the outer-most holes, you can penetrate through the floor outboard of the I-beam frame and use bolts, flats, locks and nuts - or other through-bolted fasteners.
For anything inboard of the top of the I-beams, I'd stick with the shorter fasteners unless you want to pull the underbelly down. An easy job in that drop frame area actually. Remove coroplast, remove insulation, locate gray tank, measure clearance above it, carefully install fasteners and where you can, if you wish, through bolts the brackets in the center of the tray (if you can reach above the tank).