I got the Meanwell epp-500-54 PSU installed into the ICX7150-C12. It was a tight fit, but after removing the bottom plate of the new PSU and using the shielding on top and bottom from the old, I was able to get it to fit. The switch now powers on successfully, instead of blinking orange for about 1 second and then nothing.
Thank you for all of your help in this thread! It really helped me make the right decisions in regard to which PSU to buy and how to bring this switch back to life!
I ended up going with the Mean Well epp-500-54 as well. I went a little different route getting it to fit though. I ended up grinding the 4 power supply stand offs down to be flush with the bottom case. Doing this I didn't have to remove the bottom plate from the new power supply. I did have to remove a little bit of the metal right above the AC inlet though.
I managed to find the PS in stock and it was shipped the same day from TRC Electronics for around $100.