Just an idea I have: since you did upload the Unity file in time, is it possible for someone else to build the game using it? If so, perhaps you could reach out to the game jam team and ask if one of their members can build the game and then upload it. Since this procedure does not let you any leeway to cheat (except if your evil cousin is in the team undercover, but hey…), maybe they will agree; I would try, if I were you.
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Great, then you should definitely try contacting the managers to see if they accept to build and upload! For the record, being able to run without any addition is required by the rules:
You can not require the user to download additional software from external sources (so no ROMs for emulators, or games for Roblox. If your game requires additional files (like DLLs) they should be included in the download and not require separate installation).