actually, some references mentioned to use Gr-1, however, I think it would be inappropriate to use Gr-1 antibody as it was reported before that it contains antibody for both Ly6C and Ly6G whereas neutrophils express Ly6G.
You are right about GR-1 being both Ly6G and Ly6C. If you are looking for flow cytometry antibodies, I have had good luck with this one from BioLegend: https://www.biolegend.com/en-us/products/brilliant-violet-510-anti-mouse-ly-6g-antibody-9121
I have also found that macrophages will express Ly6G along with Ly6c, so it may be worth putting Ly6c in your panels to create a negative gate.