Historically Firefox did have a GDI fallback for certain fonts specifically to address this user complaint, in order to make them look "right". I don't know when/if it was removed.
The pref name is 'gfx.font_rendering.cleartype_params.force_gdi_classic_for_families'. I believe it may have just enabled a GDI compatibility mode for DirectWrite, but I'm not sure if that uses the GDI rasterizer under the hood or not.
The pref name is 'gfx.font_rendering.cleartype_params.force_gdi_classic_for_families'. I believe it may have just enabled a GDI compatibility mode for DirectWrite, but I'm not sure if that uses the GDI rasterizer under the hood or not.