I wouldn't say you missed your boom but you did what I did "wait until I finish my degree." That was a huge backfire as I was in the exact boat you were in. You say you have years of experience under your belt and games. My question to you if that is years under your belt or is it professional "working for a company as a software engineer?" If you do have pure company experience as a software engineer then I would say whatever tests they are having you take you might not be nailing it how they want. I for one think most those tests are bogus and generic. Anyways I found that game jobs were always hiring but never hiring if you know what I mean. The same position will be there for almost a year. Don't get discouraged just keep trying eventually you will land one. If you have games under your belt no offense they must not be impressive or they would be coming for you.

If this does help I have noticed the realization of great interviewers but bad programmers amongst my last few companies I worked at. Guys would ace the test and interview but 6 months in to the job their code just isn't up to par and that is becoming more and more of an issue. You could get 50/50 on a simple question like what are the pros and cons of using a recursive function (I btw didn't know that off the top of my head 4 years ago) but nonetheless that ended my interview ASAP. I knew the pro but not the con, now I will never forget it. There is also a thing where people are not great at interviews, clam up hesitate all those are factors when hiring someone. If you answer something unsure sounds like you might be BS'ing. One thing I have also noticed is they tend to lean toward honesty. If you are honest and say I have never actually used that kind of algorithm or not that familiar with that API. Honesty is always appreciated and builds a level of trust that you don't BS with them so they know they can trust you.

Also one last thing apply to everything even if you do not meet the requirements, my friend who was a Senior Engineer at a large software company told me that and it worked out for me actually. They usually are posting their ideal candidate. Plus the interviews you can look at like experience, go in there not expecting it go in there like you are ready to learn a new challenge that you can take to the next interview.

Unfortunately there's not many choices around my area. I am nearly forced to relocate. However, one of the first things I mention in any application is that I'm willing to relocate at my own expense.

European game companies are spread pretty thin

That's funny, I have the opposite opinion of European game companies. To work in games again I got my Australian citizenship and moved from Australia to Europe (Sweden) on a working holiday visa, then looked for work. Browsing through the job ads in Sweden was like walking through some sort of magical game development company fantasy land - there were so many games companies, and so many hiring (in comparison to where I lived in AU anyway). Of course there was also more competition, but that's expected. Depending on where you are exactly the opportunities in Europe definitely are there.

From what I gather you area already in Europe? Is your country part of the EU? This makes it so much easier to relocate, and also makes it easier for a company to hire you remotely either with relocation included or with your ability to relocate yourself, as there is far less hassle with visas and such. If you are not in a country that's part of the EU you may want to consider saving up and physically moving yourself, then looking for work - I know it's a bit scary, but in my case that seemed to be the only option to actually have a company seriously consider an application for a non-senior role.