Ok, so he is in the room where his two humans spend most of their time and that's good BUT this means that he will be exposed to a light schedule that is not a strict solar one so I suggest you put a sleeping cage in the bedroom where the GCC is and a day cage in your bedroom. This way, you can leave the sleeping cage uncovered and he will be exposed to dawn and dusk and his endocrine system will be in tune with the seasons, as it should be.
His diet should consist of cooked whole grains mixed with veggies and raw produce for breakfast and all day picking and a measured quantity of high protein food for his dinner; this can be seeds, avicakes, nutriberries or pellets, it's up to you, but I don't think that pellets are the best dietary option for parrots and use a lower protein mix of seeds (for my sennies, it's the same one I use for the larger species, 50% cockatiel mix with some striped sunflower seeds and 50% small psittacine mix which is safflower-based) and a tree nut -usually, walnut or almond but also pistachio, filbert, brazil nut, cashew, etc
Now, as to getting him to bond with you, if he is already comfortable with you, guys, in the same room (which I assume he is), you should start him on a strict routine and some target training. The strict routine is so he feels more comfortable with his life (knowing in advance what is going to happen and when and then have this come to be exactly as expected gives them a sense of control. Your participation in these routines, doing the same thing and saying the same thing all the time, gives him a sense of 'flock interaction' which goes a long way toward his accepting you and your girlfriend as part of his family (timing of these activities to coincide with the wild parrots biorhythms does it, too). The training helps more you than him because it will give you a good opportunity to not only engage him in something that will provide a reward (high value item) which will endear you to him but also to observe his body language and learn how to 'read' him.
A good day should be as follows: exposure to dawn, lights on when sun is out, breakfast, let him out of his cage for flying (this will have to wait until he molts his clipped feathers) and interaction time with a 10 minute training session and just company (talking, singing, giving a treat, etc), rest at noon, interaction when bird becomes active again after the noon rest (around 2 pm but it depends on the individual), training session, company, flying time and training session right before dinner, turn off artificial lights when sun is halfway down to the horizon, serve dinner in sleeping cage, allow bird to eat dinner and roost and go to sleep when night falls. Now, I realize that this does not quite 'match' your own schedule but, unfortunately, birds are not like dogs and cats that adapt to our lifestyle, we need to adapt to theirs.