I am not 100 percent on this....but it is my understanding that Oakwood Cemetery does not have a burial list from actual burials at the time.
I was told that years ago, seventies I think, a man from Slema compiled a list from hospital records he found at the ADAH and ordered markers from those lists and had them placed at Oakwood and that's where the markers in the confederate burial section came from. I have discovered several markers there for soldiers who survived their Montgomery hospital stay and went on to survive the war. I'm sure many did die and are buried there that have markers. Many are unkown markers or only have a name with no unit, or a unit with no name.
Perhaps Alan Pitts or Bob Bradley can assist you on how to research the ADAH for hospital records.