How do you maintain a balance of selfless service and career progression?

Unless you are -exceedingly- lucky, nobody is going to fight for your career advancement for you, so you have to fight for yourself. Selfless service doesn't mean letting opportunities pass you by.

If you really believe in selfless service, get your promotions, and use them to lift up others. Get your education, civilian and military, and use them to teach others. Look at Army Career Tracker to see what assignments can help you move along. Get ambitious in your career field, volunteer for boards, competitions, etc-- and share what you learn along the way with the new Privates and Specialists who have the same desire.

I've been in E7 slots for years, and am still stuck as an E5. I know the pain. Don't get stuck in a rut, fight to move forward, and bring everyone you can with you.

Making yourself a better Soldier and ready for promotion is not necessarily in conflict with selfless service. In fact, there is great synergy there.
You become more valuable to your unit, and you will earn you way up the ranks.
Just ensure that the career progression doesn't become a priority over your Soldiers, and you'll be fine.
You men always come first.

Easy, you use selfless service as career progression. I have seen a lot of ass kissers, brown nose individuals and D*** S***ers my entire career and they know who they are but you have to not let at whats going to get you the edge or how can you look good by undermining this individual but you have to put every thing and one that you are responsible for first and always strive to make your organization better and more efficient for everyone. Anyone can wear a SGT rank but it's until that individuals actions are observed is when you know if they're an NCO by their leadership because thats what we do and who we are, "professional, Noncommissioned Officers, leaders!".