You have 'Cloth drawers" ... and can't make them smaller? Not sure I understand that statement.
But, if it were me, I'd take out the drawers, get new one's made that clear the floor, and install half-inch insulation board on the floor, then cover it with carpet or laminate flooring.
Linoleum has no insulation value - so is worthless for floor covering.
No good way to insulate under the vehicle without hazards like muffler heat, etc. Insulating the floor will lose an inch, but gain everything you need and in the long run, a better safer way to save heat.