is there really no way to save partway through a day? not everyone can finish a play session when the game wants you to?
That's correct, you can only save at the end of the day. The reasoning behind this is that it would have required a significantly more complex save system able to account for saving each individual dialog choice and repopulating each of them every time the game loads in, which could create a good deal of technical issues given it loads everything in at a scene's construction.