Never glue the floorboard carpets in. The original carpet is permanently afixed to the floorboard under the seat railing; I, however even have mine rigged to Velcro in place with some slits sewn in for removal. Not just rain, but washing will always leave water on the floor, and RUST.
Complete kits are available for the install, TRF has some nice ones, even in wool, if you want plush. I coated the entire floorboard of my TR6 with a thick coat of PPG epoxy "paint" so that rust should never occur. The same stuff they use to coat oil rigs offshore.
Bill