Your quest is well written and honest. After having lived in Manhattan 3.5 years, Boston 6 years (on and off), Jacksonville, FL (1year), N.J. (1/2 year), VA (1.5 years), I don't know why you would ask for food like that (bad food). You're in L.A. to get away from that type of food. I didn't know I was spoiled having grown up in L.A. since 1969 and had to move around for work. Those take out restaurants you're talking about are terrible. I'm not trying to chide you, I just have to express my disappointment. Those aren't really "old style" Chinese restaurants - they were simply makeshift recipes and policies to conform to the misguided expectations of the patrons.
I must however admit, sometimes, I satisfy a craving for some food I've had as a kid - analogous to your need for NY Chinese food. So I heat up a can Chef Boyardee's Ravioli's with cut up slices of hotdog to accompany a tray of Banquet's Salisbury Steak.