Fighting HR Rules for a promotion

Posting here because I actually need feedback and this is the most active forum.

I am an analyst in CB in a development program. There is an opening that would be a promotion for me right in my office, but HR is not really allowing me to apply due to their timeline rules (that's a whole different story).

I think i am totally qualified and ready for this position, but cannot be considered due to HR. I am thinking of going to my manager and very clearly stating: "I think that i have earned consideration for this job at the very least. I earned the respect of my team and our other partners, so i would appreciate your support in letting me apply and compete against other candidates for the spot. If i am not the best fit, fair enough, but i think i will be."

Any feedback from managers who would receive this message, or people who have been in this situation?