Well back when younger there was the joke about putting 10lbs of PooP in a 5lb PooP bag and that is where you are for sure. No way to put 550Gb into the space allowed on 120Gig SSD.
It sounds as if you likely need to install only the SSD and install Windows on it and then after hooking up the HDD again >> make choices as to where you are going to install the game and so forth whether onto the SSD or onto the original HDD after it is formatted and extraneous data removed.
Just a note. I have been doing this computer thing for a number of years. Back when I was learning; it was told to me to treat data on a computer as a file cabinet. So I have partitions for Operating System, games, photos and general data and thus I can do things to the O/S partition and not be actually having to deal with the other data. If you had your 1TB done thusly, then you would have far less size to be moved.
RGone...