What do aircraft designers like Burt Rutan do to cheaply practice geting good at designing aircraft?
Let's look at every of your concepts:


Joining a large company: As you noticed yourself, you won't get a broad range of skills, but a deep understanding of a narrow field, unless you rotate between departments every few years. This will be hard to pull off, and will take time. If you are good at what you do, your boss will try to keep you (they always try to promote the duds away in big companies, and the good people get stuck. Really!)
Building RC models is great if you want to become a configuration expert at low speed aerodynamics. You will gain no experience in transsonic aerodynamics, structure, systems - 90% of the needed knowledge cannot be gained from model aircraft. But after 20 models you will be great at understanding flight mechanics and the pros and cons of different configurations.
Forget flight simulators. Things only get interesting once you leave the realm of attached flow. Stalls, spins, flutter, oscillating shocks - that is what you need to understand when you want to do good work, and flight simulators will not teach you this. At all. Also important is to understand the effect of single failures on the whole aircraft, and designing for robust response. Again, no simulator will give you anything even resembling a realistic response.
Hybrid: Now we are talking: Keep your eyes and ears open! Visit conferences, museums, exhibitions and talk to the people. Get a pilot's license and fly yourself! Read books and technical reports. Be open to all things, be it metallurgy, fuel chemistry or whatever. Try to do stints in workshops and flying clubs. Volunteer for workshop duty and do maintenance and repairs. Don't be shy to ask, and if you see something strange, don't stop until you have arrived at a convincing explanation. Do this 10 hours a day for 10 years, and you will collect the necessary all-around knowledge.


The best way will be to participate in as many aircraft design projects as possible, from start to finish. This has become extremely hard, and some engineers will spend their whole professional life working on just one design. Let's face it, the golden days where you would work on a new design every year were maybe 80 years ago. On the other hand, the Internet can bring you an incredible wealth of information and past experiences from which to learn. Like this site. Use it!