You have the saponification correct above. However, some of the PET will be partially saponified and the phthalic acid in this case will be attached on one side to the ethylene glycol and the other end will be free to grab gelatin. This is a very efficient way to create the adhesion we want. OTOH, you have to remember that in all of these methods a thin layer of PET is destroyed. The choice then is to choose the least harmful method.
In the case of NaOH, didn't you mean NH4OH? Sodium Hydroxide in excess will cause extremely rapid development that leads to fog, but alone it does not cause fog. In fact, I doubt if there was enough residue in your tub to cause any problem at all. NaOH washes out very rapidly and completely with just several changes of water.