It was always a thought of mine that when the day comes to replace our front cab carpet, is to order an OEM rubber floor covering direct from a Ford dealer parts department. It will include an insulation blanket attached to the underside which should quiet down the ride a lot and also control cab temperatures better. Being black rubber, you would loose the home-like feel, but I imagine the benefits would outweigh the lack of visual appeal.
You'd likely have to tell the parts guy you want a rubber floor covering for a box truck of the same model year, 2005 in your case. If no longer offered, then "up" the model year to one that is less than 10 years old, so say "Box Truck 2013".
If you remove your current carpet, you will find it to be very thin with no insulation properties. The carpet has to be very thin in order for the RV manufacture to conform it to the irregular shape of the floor pan, making many cuts and folds, and gluing it down to the steel floor. But buying a preformed insulated rubber floor covering from Ford, theoretically it will fit like a glove with no messing around.
I don't know if this is possible, but when installing the rubber floor covering, I would first attempt to install it over your original carpet specifically to gain the extra insulation. But if the rubber covering isn't fitting right because of the carpet, then rip out the carpet for the right fit.
There are also aftermarket suppliers of floor coverings like the example
SEEN HERE offered as carpet in various colors. Maybe this is worth consideration.
