Normally, ANACS will not put a descriptor like RPD on the holder if it not significant and obvious to the graders. Think hot lips that the sender doesn't ask for attribution. ANACS will likely say something on the holder like doubled obverse while not calling it a hot lips. I would suggest searching the 1880-S VAMs on Vamworld in the Top 100, Hot 50 and Hit List 40 coins.
I will try and help. First of all, cracks will not be listed. They may be shown on the VAMWorld pages, but will not be in the listing. They are too weak on your coin to be called breaks, which are listed. The doubling under the date digits appears to be machine doubling. When you go to the VAMWorld discussion forum, there is a post at the top entitled "Do You Think You Have a Doubled Die". Look at that. Finally, the date placement appears to be a Near Date. Look at the listings that start with a near date as an attribution point.
The "doubling" on the reverse appears to be machine doubling, not die doubling. Notice the flat like shelf to the lower portion, plus all the "doubling" is in the same direction. Lastly, the mint mark has this "doubling" as well. The mint mark was hand punched into the die after the die was prepared so it could not be die doubling. Machine doubling is very common.
The date digits look weird and the mint mark placement doesn't look like any identified VAMs as far as I can tell. As mentioned, the toning looks off and common to the China wave coins. I say fake.
These are fairly common. I wouldn't spend my money to have them slabbed and attributed. There really isn't much, if at all premium on them IMHO. While they are cool die varieties, you could likely pick 3 to 4 off Ebay at any time.