Your best option is to have the carpet carefully removed and rolled up for storage. There are laminate floors that snap together rather than glue or nail. Such a floor is easy to install, and could be removed and reused at a different location later. The carpet could be re-installed by a carpet installer, and would be unused and undamaged. Shag carpet and pad would probably have too much flex for a floor to be installed over the top, but removal does not mean you have to throw out the carpet. Just store it for later reinstallation. Discuss your plans with the landlord. As long as you don't have other tenants living below you, its hard to imagine why the owner would object. Michael Holigan describes an installation of BHK Laminate at the following link: