What career option is the most viable if one has very wide research interests?
My best advice, though it might not suit everyone, is to pick something, anything, that you are willing to work very hard at for a decade or so and become an expert in that field as an academic (my choice). At that point you can probably get tenure and with tenure you can set your own research agenda, more or less. But your ideal academic job may or may not be in your current country of choice. 

In some academic jobs you can set the research agenda completely yourself, though you may need to convince people that you are contributing to the mission of the institution. But if you are a mathematician who made the grade in, say, topology, no-one will be likely to tell you that you need to keep doing topology, and few will tell you that you can't branch out into applied fields, or even quite different fields for at least part of the time. 

And, in fact, many academics do change their interests over time, even if they stay fairly close to the core field they started in. 

But an industrial job, now-a-days, comes with many restrictions on what you can do and many requirements on what you must do. The days of old in, for example, Sun Microsystems or Bell Labs, are over. People in the successors of those places generally can't just think deep thoughts and try to build something interesting. But even in those old style labs, the people permitted to do that were few and had already risen through hard work in the lesser jobs for some decades that left them at the top of the heap. There are surely exceptions, but I think very rare. 

But the bottom line, is that if you want to be a polymath, then you need to work very hard to build a reputation that lets you have the freedom to do what you want. It is just more accessible in academia, I think.