Measuring position in a room with mics synced with GPS modules in the corners, with 1 or 2 on the floor

Unless you have a way to measure the radiated power from your device and keep it the same as you change antennas, the project is hopeless. Anything different than a 1/4 wave antenna will automatically reduce the radiated power, so you will have to increase the transmitted power to make up for the loss at the antenna.