And the results are: I hope you have strong teeth.
I feel quite certain that either I did something wrong, or that the Chi-Chi's version contained obscene amounts of preservatives.
I should have done some comparison recipe viewing - the recipe I used didn't have any kind of fat in it (besides the milk). All of the other recipes I found (after my dismal failure) contained shortening. I'll keep trying - and when I've found a winner, I'll share it!