What are the proper steps to take if you've been neglected for advancement due to mission tempo or just pure neglect?

As a young Non-Commissioned Officer, I'm sure you've heard the expression "squeaky wheel gets the oil". If not, I'm happy to introduce it to you. The other end of that spectrum is that if the wheel kept squeaking, it'd be replaced.

No one cares as much about your career as you do. You have to speak up and go about things the right way. Utilize your chain of command and voice your concerns. As NCOS, we sometimes lose sight of taking care of ourselves in favor of caring for Soldiers.

I noticed a couple of "almosts" in your question. Leave no stone unturned in your quest for promotion ponts. Complete those almosts and keep pushing, you never know when those points may drop. Good luck and please reach out if you have any questions.

You stated you used the open door policy, what was the outcome? Was it about the promotion. Ask to review your counseling packet for justification. Sometimes we feel that we are doing all the right things but if you have not been counseled or led in the right direction there might be something missing you don't know about and are not aware of. Asked to counseled so you may know what you need to do. Excel at your additional duties, excel at pt and weapons but most importantly don't lose sight of your soldiers. In your concerns for yourself you don't want to forget about them. Be patient and be a great and knowledgeable Sergeant before you rush to be an average Staff Sergeant.

I'd first read up on AR 600-8-19 to make sure I had my ducks in a row. Tear through your ERB for discrepancies, DOR, PEBD that may show you ineligible, if any old flags were still showing that should have been lifted, your correspondence courses have been coded, etc.
Administrative stuff like that will kill a promotion faster than a poor showing at a board.