The unbearable projectivity of being a good moduli space of Gorenstein curves of genus one with non-colliding markings

We classify all open substacks admitting a proper good moduli space inside the stack $\mathcal{G}_{1,n}$ of log-canonically polarized Gorenstein curves of genus one with $n$ distinct marked points: they are exactly the stacks $\overline{\mathcal{M}}_{1,n}(c)$ defined by Bozlee--Kuo--Neff. Restrictin