So far I have about 80% of the project done. The mirrors work so well when they are turned on and definitely create the desired infinity effect! The big things I need to figure out are how to 1, get the clock to be more apparent when the LEDs are off, 2, wire the LED strip to run off battery power, and 3 final touches to clean up the design. Below is a picture of the clock turned off.
The face of the clock is a bit more distinguishable in person but still not to the caliber I am aiming for.
To end on a good note, here is a video of the best part!