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 running a project... why not run your own project. Do consultancy on the side (even to your existing employer), but get out and do your own thing.
In time, you'll hire your first employee, then your second etc. There is far more career progression when you're growing a pyramid beneath you.
This was absolutely my solution to the same problem.
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 ;-)
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 running a project... why not run your own project. Do consultancy on the side (even to your existing employer), but get out and do your own thing.
In time, you'll hire your first employee, then your second etc. There is far more career progression when you're growing a pyramid beneath you.