You are in no way competitive for the legacies.
Military experience is a good resume box to check (especially if it was PAST experience, vice currently active guard/reserves). But it will not make you special...there are plenty of combat-experienced military pilots with all kinds of management/staff experience.
To become competitive you need several thousand RJ PIC, check airman, and whatever misc. items legacy HR folks want to see (volunteer work, high productivity, etc). Oh yeah and > 3.0 GPA and no checkride busts seems to be important too.
When you are competitive relative to other RJ drivers the military and management experience will help. It will not substitute for the usual civilian-track qualifications (ie no shortcut).
Highlight the safety management stuff when the time comes.