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Otherwise my other option would be to hook it to a computer monitor here at work, but from what I've gathered, that would involve modding the box so that it will only work with a cpu monitor
Not true. Really its just a matter of how much work/money you're willing to put into your xbox. There are two ways to achieve hooking up your xbox to a monitor (and none are permenant).
The first is to just buy an X2VGA and component pack for the xbox (or something similar, this is just the best from what I've seen). Quick and easy, no soldering involved and as soon as a regular composite pack is used its completely usable on a TV.
The second (and cheapest) way to do it requires opening up the xbox and soldering directly onto the motherboard. Following
this guide you can solder in a vga port and switches (though, you will also need a vga compatible bios) which will enable you to use your xbox on a PC monitor.
If you have any specific questions let me know.