There are no known Prooflike or Deep Mirror Prooflike specimens of the 1900-O/CC. I personally have never even seen a Semi-Prooflike.
The 1900-O over CC Silver Dollar is exactly that...it shows a New Orleans mintmark punched over a Carson City Mintmark. How could this be, when those two mints are so far apart? Actually, the Philadelphia Mint was responsible for making all of the dies used in all of the mints, including the branch mints. Thus, Philadlphia sent dies with O mintmarks to New Orleans and dies with CC mintmarks to Carson City. However, the Carson City Mint made no silver dollars after 1893, so there was no need for Philadelphia to send dies there in 1900.
Curiously, this error was made on more than one die. Were the 1900-O/CC Dollars made using old leftover dies from years earlier, or did an engraver make a mistake by punching a CC mintmark into some reverse dies in 1900?