This doesn't answer your question: Is pirating an option for you? You might be able to grab them more easily that way

My understanding is that original Xbox (and other consoles) need to be modded in order to run discs that aren't original. If you're going through the trouble, you could add a bigger hard drive and just load the games into there

Original Xbox? Why worry bout optical drives just put large HDD in it and load all the games on that then keep HDD backup.

Yes, optical drives can just "go bad" while sitting. Even if not the laser, many of the mechanical parts can age and fail.

There is no "set it and forget it" medium in existence. Multiple copies, in multiple locations and if possible on different media types.

How do you plan to store the console? Maybe some sort of vacuum/gas filled seal would work? This is just off the top of my head since I haven't researched it, but vacuum sealing it with a desiccant pack might be useful here. For gas I'm not sure what you could use that's common but maybe helium? You would have to worry about a slow leak over time though.