Alright, so... I did end up getting it working eventually but unfortunately I'm not even sure why it does now. The things I tried:
- Toggling Admin access on the Sandboxie Steam instance
- Replacing Sandboxie Plus with Sandboxie Classic
- Toggling x64 Bit Executable in GMS 2
- Toggling Sandboxed File System in GMS 2
- Toggling Alternative Steam Launcher in GMS 2
Hope any of these (or any combination of these) helps.