It's like reading an Ask HN from me. You sound like me about 3.5 years ago. I was in the same situation, dev lead for 10 years. Bored. But I hated shuffling papers more than I hated being a drone...even if I was a senior drone. What you need to do is start your own Startup. What you're lacking in experience is only a problem if you need to actually manage people. You must likely have plenty of experience actually run…
I'd been a solid dev for 10 years and the closest I'd come was being an unofficial team lead a couple of times. I found it hard, in a big company, to work on raising my profile without feeling like I was taking credit for other people's work. Sadly, it's hard to get recognized as being a "leader" if you are scrupulous about acknowledging the efforts of your team -- even if your team-mates recognize your leadership role, nobody asks them.
I'm also, frankly, an insubordinate bastard -- I always get along really well with my immediate manager and co-workers, but upper management tends not to like me because I poke fun. So it's easy to see why nobody was running to promote me, and I can't say I really blamed them.
So I jumped at the chance to be tech lead and co-founder of awe.sm. Now I have my own team, and I am getting to prove my leadership credentials first-hand. I'll let others decide how well that's going ;-)