There is no "best" solution in general, what is good for one person is bad for another.
There are several important parts to your short message.
You write that there "aren't many game development jobs here", which means there are some jobs. Networking (talking with people, not using cables) is the absolute best way to get a job. Find out who works there, talk with them, make some friends, and let them know you're interested. When the boss say's they're thinking of hiring someone you want friends at the company who will suggest you before the job is even opened to the public.
You didn't mention where you live, and that makes an enormous difference. You need to be able to compete with others for the jobs. Since there are few game development jobs, you will probably need to apply to jobs that are distant, and be prepared to move if you get them. If you are in an area with high competition for those jobs you'll need to have demos or a strong background that can showcase your talents. In other places of the world there is little competition.
As for the transition, I'd consider both a direct jump and also a set of transitions. There is a great book out there, "What Color Is Your Parachute?" that discusses the topic at length. From what you've described you have at least two transitions to make. You might be able to find the job that you want directly, so apply for that. But you might also have success in a multi-stage transition. A transition first to backend programmer in business, then a second transition to backend programmer in games, and possibly a third transition to front-end developer in games. That could take several years to complete, but could be a viable path if the direct jump won't work out.
And as for learning to program in a more elegant way, that is good. Always keep learning. This is a field where you must continuously train and retrain yourself. Much like doctors must continuously learn new treatments, lawyers must continuously learn new laws, mechanics must continuously learn new engines and auto types, computer programmers need to continuously learn new programming languages, new programming tools, new technologies. Keep learning while hunting for the job, and keep learning even after you have the job.
Good luck on your job hunt, I know it can be difficult. It can also take a long time to get the job you want, and may require getting jobs that you don't want until you get the one you want.
