XBLIG might be an issue for the BadUpdate exploit.
- You need the full firmware Update installed (full = with avatars etc.)
- The XNA Indie Player Title Update must be installed
- Here comes the dangerous part: In Dash Launch you need to activate contpatch and fakelive.
I don't know if these patches write to the NAND - if they do, your 360 won't boot after a restart - if not, then you might have a chance to get XBLIG to run.
EDIT:
MrMario has a video tutorial for XBLIG and in the end he says that the Dash Launch settings are not needed - maybe you are lucky:
EDIT 2:
Maybe not, a comment said that it doesn't without enabling the fakelive option in Dash Launch.
Wiki also says that fakelive is needed for Indie Games
https://consolemods.org/wiki/Xbox_360:DashLaunch
Enabling fakelive kills Proto support tho, so pick your poison.
Also keep in mind that I don't know if Dash Launch applies these patches dynamically in RAM or permanently in NAND - be cautious.