Part of the problem is you are using a Surface Pro which on the current Intel chip does not support any sort of connected standby or ultra power efficient mode. You basically have awake w/screen on, awake w/ screen off, sleep, hibernate and off. This doesn't make the Pro with a core i5 processor the most efficient mp3 player. However, it seems that is understood and the basic question is how to quickly turn the screen off.
Since you are running Windows 8 you can get a program which will let you set a hot corner as you already mentioned. The issue with that is it will only run from the desktop so you must return to the desktop from the music app (or use split view) to have the hot corner work and shut the screen down. Another option is to create a custom keyboard shortcut which will run the command to turn the screen off or switch to a low power profile with a quick screen time out. This is probably going to be your best option since a keyboard shortcut should work from both Modern UI and desktop and is quick and easy. The limitation here is that you need to have a keyboard to perform the shortcut combo (not so good if you are using in touch tablet mode).