I think simplifying the system to something like the system used by British Army could work:
Private (held by recruits and "rookie" soldiers, no insignia, E1-2);
Lance Corporal (Fireteam Leader, internally E3 but E4 to E5 for US equivalence, one chevron);
Corporal (Section Leader; internally E4, but E5 to E6 for US equivalence, two chevrons);
Sergeant (Platoon 2-i-C, internally E6 but up to E7 by equivalence*, three chevrons),
Staff/Colour Sergeant (Company/Battalion Staff, 2-i-C in some specialist units like the MPs, mostly E7 equivalent, three chevrons with device);
Warrant Officer Class 2 (Drill Sergeants, Company SGM and similar, custom device);
Warrant Officer Class 1 (SGM Instructor, Regimental (and above as needed) SGM, Garrison SGM; Bandmaster/Conductor and similar, custom device).
*Mostly British Army, Marine Sergeants may also act Troop Commanders roughly equivalent to Platoon Leader.