I would strongly suggest try riding on the lunge line as well, without reins. This really really forces you to think about your seat, and push that tush down into the saddle.
Balance is more than just not flopping around in the saddle. It involves your ENTIRE position, not just your seat. A good rider will have good balance, which means relaxed shoulders, quiet hands and quiet seat, firm, quiet legs (not gripping, but relaxed and not moving around), eyes up, good posture, etc. Balance is about being in tune with your horse, moving with his movements, completely in sync with him. Now obviously this is something that takes work to achieve and I don't think that any rider can ever have perfect "balance," all the time since every horse you ride is different.
So yeah, lots of time and practice, riding different horses and riding on the lunge without reins should definitely help.
Would love to see some videos as well! Good luck, and I'm sure you're doing great!