Travis,
I'm not sure about the hospital register. There are many hospital records in the National Archives and they have NOT been microfilmed so it would require a trip to DC and doing the legwork yourself. The only book that I have lists Confederate records in the NA and there are no listings of hospital records in the New Orleans area, only from Shreveport. Typically, if there were any hospital records in RG109, they would have been included in his CSR as a card reference so that may not be the case. You may try the Miss. message board to see what records may exist for the cemetery. Also, perhaps there is a sexton's record at the cemetery or something. Like you, I would like to believe that one died in New Orleans and the other at Okalona and the family had the foresight to move the one from New Orleans to be by his brother, if that is what they were and at some later time, CS headstones were placed by third parties. That is the most logical explanation but who am I to say for sure? Check the cemetery to see if they have any dates of internment or is it just records of plots, if any records at all. All there may be is just the headstones.

I don't think that he was sick in New Orleans and they were moving him to Okalona. There would have been no reason. His brother ( I keep saying that but not sure the relation) would not die for 3 months yet so family, if anything, would have moved him to home. It just seems probable the other scenario with both dying and then family moving one to be near the other. I have no other explanation.

As far as Cypress Grove, the burials list came from a listing that is kept by the New Orleans Public Library. That is where I transcribed from.

Sorry to have not been of more help,
Wayne