(not sure if I'm the first to notice)
If you select either reverse/hardcore modes in an existing save file and then start a new game, the mode will stay the same even though it hasn't been unlocked (a similar thing can be done in cuphead where you select the expert mode).
Maybe a hardcore run from the start is possible? I haven't tried, but theoretically it is
Oh, I didn't understand your question at first. It can be any one of the three save files. I guess the mode is just stored globally and only changed when you press one of the buttons
Edit: I think it should be called the "Fresh Hardcore" glitch. Reverse is redundant pretty much (it is called Fresh Expert Glitch in cuphead speedrunning)
I don't even think it has to be a new save file. I think you can do this for any save file regardless of completion