If the number of songs in your list hasn't changed, I'm quite sure you can just play, on random, starting at the first song you remember; the random function isn't very random. I used to have a sweet series of songs that played if I started with "She Dumped Me" by Gus and Frank.
From what I can tell, the algorithm advances a certain number of songs, and if there's a different number of songs, it'll play other ones to those you want.
...and this time remember to put each one in a playlist as it plays.