@Coinbuf- I ended up not sending in the quarter for the reasons you mentioned. I did submit the halves and if I am wrong then I guess it will be a learning experience. I am fairly confident they are DDOs because, as you said, there are splits on the serif. The other obvious indicator, imo, is the split on the base of the 4.
@RWBI appreciate the resources. I think it is funny that they rules for the signs of what is a DDO change depending on when the coin was minted. Especially when it comes to copper coins in the mid to late 1800s. The flying eagle and IHP ddo's I have seen seem to have clear "shelves" which are indicative of some other cause of the doubling, o. I also wonder whether that 1920 isn't also die erosion and not "strike doubling" but who knows.