Good luck OP, but no one is indispensable and others could be trained to do the work...promotion may never happen, no offense. Hope you get it!

"I think it's in his best interest for me to get the promotion because he should want me to stick around to keep doing the work. No one else knows how to do the work that I do"

OP again. I would still be under the boss and on the same team if I got promoted. It would basically be a title change and more money, but the work would stay the same since I'm already performing at a higher level than my current job. I think it's in his best interest for me to get the promotion because he should want me to stick around to keep doing the work. No one else knows how to do the work that I do, so he would have to do it himself or invest the time to train and oversee someone else. I think the promotion problem is at the agency level, not with my boss.

Keep in mind the possibility exists that your boss really doesn't want you promoted because then who would do all the work. When I first met my husband 15 years ago he was the nice guy who stayed late and did way more than his fair share. He kept telling me he was going to get promoted and I gently told him it might not happen. He then took classes at night to get his teaching credential. When left his job two years later to become a junior high school teacher he still hadn't got promoted. Only then did he realize his boss was sabotaging his promotion when a supervisor told my husband that it was too bad he never wanted to change departments and work for him.
So now he works late while other teachers leave early, but at least it is a rewarding job for him.