https://dl.dropboxusercontent.com/s/3qqhnwpyniyn5dl/ocremixlinker.html
It just links to a random remix based on the number from 00001 to whatever you put in the max number field. Currently it is 2959, though I will try to update it occasionally. I probably won't do that very well, but here it is if you want to use it.
I do know that the front page has a few random remixes, but they don't change when you refresh, where as this one is very unlikely to give you the same ones.
Hope someone finds this useful, and that I posted this in the right section.