There's no code requirement for the GFI to be in the load Center, it's more there just for convenience and most installers use that as the GFI for the pool lights.
You should have enough room to mount the Transformer inside and still keep the GFI outlet if you used a small extension for the outlet itself
You should have enough room to mount the Transformer inside and still keep the GFI outlet if you used a small extension for the outlet itself