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[boflc]

without a jtag, you cannot run games without a disc in the tray.

with a stock console, you can install the game to a hdd, but the disc must be present to authenticate, in effect, your license to play the game.

you could try the "pretty please" route with microsoft or the developer -- the latter has shown to be effectively more than 0% of the time via social media, but you need to be clever about how to get the dev's attention.

beyond that, you'll need to start socking away from money for a new copy.  your experience is exactly why folks modify their dvd-drives to run custom firmware from c4eva, rip their originals to ISO's using an 0800 drive w/XBC and run their games via DVD-DL's they've burned.  oh, and originals are kept in a safe place (away from kids!).

[Aldanga]

If you don't have a physical copy, you cannot legally play the game. That is defined as piracy, which is not supported here. Enjoy your vacation.