Hey Liberty,
Your ambition and eagerness is great, but I think you are overthinking this.
The majors don't know which flight departments are good and which are bad. They don't know if flying a citation X or GIV is more prestigious. They know total time, PIC time and additional duties AKA director of safety, chief pilot, etc. At the regionals or in the military they are more opportunities to put extra stuff on your resume. Even trivial "special projects" stuff counts.
I think that the 121 badge would help, but an additional title at your current job would be as beneficial, even if it's unpaid.
My $.02