As previously stated, the use of a heat gun and scraper will allow you to effectively remove your carpet from the F/G skin.
The heat should be directed onto the adhesive itself. As you pull on the carpet the adhesive will have a tendency to stick to the carpet and F/G and separate cohesively ( it will start to string out). The scraper will be able to cut these strings. This is probably going to take some time, but it will work. During this process, you'll develop a feel for how much heat you need to apply and the length of time needed.
I would not use any flammable or non-flammable solvents in the cabin area, for this application. Most flammable solvents have a flash point around 32 degrees F or below. This simply means that you run the risk of an explosion or fire if the vapors are subjected to an ignition source like a spark or flame. Plus, most solvents flash off too quickly to have any lasting effect. They will soften the rubber on a temporary basis, but it will revert back to it's solid state as soon as the solvents evaporate. If you wanted to use a solvent, you would need to use a product like mineral spirits since it's evaporation rate is very slow and it's flash point is around 106 degrees F. At least it would have an opportunity to soften the adhesive so that you could remove the carpet.
If you wanted to use a non-flammable solvent such as methylene chloride, these pose other risks. First of all, the chlorinated solvents are known carcinogens. They would also evaporate too fast to have much of a lasting effect on the rubber before it reverted back to it's original state. Secondly, their vapors are heavier than air and as such will build up from the floor upwards. The more you use, the greater the build up. In addition to the vapors being carcinogens, they are also good de-greasers/paint strippers and corrosive to paints, vinyls, adhesives, etc. Which means that they could effect o rings, hoses, paint, adhesives, mechanical equipment and electrical equipment. If they are used on a very limited basis, you should not have those problems.
Bob