First the bad news: you are not, and probably never will be, "done" with the dull boring big name clients.
You are in business, not indulging in a hobby. Those dull clients are the ones who will probably provide the income which makes it possible for you to experiment and branch out into other areas.
Those bleeding edge people in other industries will nonetheless be impressed to know that big name corporations have enough confidence in you to use you for their own websites.
Even if you don't want to point to specific pieces of work you've done, it's well worth being able to say that "ABC Inc" and "XYZ Ltd" are major clients of yours. Though be sure to check with those clients before citing them as references.
As to breaking into new industries ... you need a reputation as someone who can deliver on-time and on-budget. Small bands etc will have limited funds. Then you need to have a portfolio of 'sample' sites you can show them. These should be sites which implement themes etc close to some of the more experimental ones you've already seen.
And yes, networking is going to be the real key to breaking into a new industry.
You need to trawl business sites (NOT Facebook et al) like linkedin for potential contacts, then use those sites to gain introductions. Perhaps pay for a premium account to get better search capabilities.
Go to trade shows (not sure what there is, but there's bound to be something). Have a business card printed up, and leave it whenever you get the chance.
But through all this, keep doing the dull, boring work for the recurring customers who are paying the mortgage.
As an example, I was a freelance/contractor for 15 years and rarely worked in the same industry twice. I've done everything from heavy industrial, through defence, and on into consumer products. When I was flush, I played with the startups or did some proprietary work - but I ensured I had a backlog of 'regular work' to fall back on at any time.