I have the same problem with my carpets. I was thnking of getting a new set of carpets and instead of just putting them in place, secure them properly as there must be some product out there to do so. However, I want to be able to release the carpets as well so that I can keep an eye on whats underneath to ensure no rust is developing.
I tried heavy duty velcro i stuck it on the back of the carpets and on thr floor, i thought it would come off the floor first but its still stuck fast but it keeps coming off the back of the carpets >

i think its because my carpets are really rubbish though because the velcro sticky pulled the backing off them. if your carpets are clean and not falling apart like mine it would probably work!