for the specifics of Day 15 problem I think that most people (including myself) did not use an OrderedTable, instead they used a standard Table[int, int] with key as number and value as turn last seen. You would also keep track separately of the last element.
As far as I know the use case for OrderedTable is not to be able to extract elements given an index (like last index) but to be able to have a reproducible and consistent ordering when looping over keys.