I was in near enough exactly the same boat, except I am a UK student.
I graduated with a Psychology degree from Manchester Metropolitan University and then got onto a BSc (Hons) Computer Science at the University of Sheffield. I did it for about two weks before I realised I couldn't afford the travel (I was commuting from Manchester) and could no where near afford the fees. You do not get funding from the government if you have a degree.
I took a year out and found the conversion courses. I applied to Bristol, Birmingham, Imperial, Sheffield (slightly different course), and Liverpool. All Russell Group unis, if you place any importance on that.
Any I got into Birmingham and Liverpool. I would have loved to go to Birmingham, but I can stay at home with my partner if I go to Liverpool.
The point of telling you my life story is that I am so glad I am doing it this way. Even the first week of another BSc was torture. It's full of freshers who don't really care because it's first year for them and most of them aren't self funded. I am generalising here, obviously not all freshers are like that.
I highly recommend doing a conversion, why spend 3 years doing what you can do in 1! I emailed lots of PhD programmes (including the likes of Oxford and Manchester) and employers, and they all said that they would consider me with the MSc conversion, providing I performed well enough.
I hope this helps somewhat, if you have any questions about applying or anything then please feel free to ask
Good luck!
Edit: My desired area of expertise is also game programming and robotics so those were the types of employers I contacted. They stressed a lot of imporance on work experience, so keep making games as well. Lots of them did say that some sort of qualification would almost be a pre-requisite, but wouldn't get me anywhere without work experience. I think it's brilliant that you are doing this with your girlfriend. My partner and I are a similar team!
I also wouldn't bother with a game specific course, from all the information I gathered, gaming companies prefer straight computer science courses as they teach you more general skills that allow you how to learn programming languages, rather then teaching you a programming langauge. If that makes sense