Career Guidance Please!

Great question, but I have a slightly alternative option for you, have you considered "serious games"? That's the industry I am in. Also might be called simulations or e-learning (which are broader in definition). Like you I have a background in engineering and this route can bypass the extremely competitive area and requirements of entertainment games which everyone and their dog wants to get into. In my case I fell into it by accident but I mingle in game developer circles and have as much fun (well depends on the deadlines) and personally I think it can be more stable for job security (although nothing is guaranteed in any industry). There are differences in approach obviously but you're using the same tools just with a more specific end goal for the user in mind, and there is more and more gamification even in the most serious industries nowadays, I've even been able to buy games and put on expenses for research purposes!

As far as game development specifically I will give one piece of advice (from being on hiring end too, I work with people that used to be or still are game developers in their own time) and that's to keep learning what's going on with game tech, learn the tools (keep practising with Unity) and start creating. No amount of qualifications will be equal to being able to demo your own stuff working! Portfolios again and again are the best way to assess someone in many creative industries.