I'm a tonsured cantor; I've been through Royal Hours several times, and here is my take:
Royal Hours are part of a paramoni. There are three of these in the liturgical year: for Christmas, for Epiphany, and for Pascha (the Paramoni of Pascha takes place in the context of the Paschal Triduum, and is not named as a Paramoni).
A paramoni is never celebrated on a weekend; therefore, if Christmas or Epiphany falls on Sunday or Monday, the Paramoni, and hence, the Royal Hours, is celebrated on the preceeding Friday; otherwise, it is celebrated on the Eve of the Feast.
Royal Hours (so named because they were a special service composed for the Byzantine Imperial Chapel) differ from ordinary Hours only in having a more set structure of fixed psalms, Gospel readings, and a special idiomelon sung at the Ninth Hour with prostrations. In parochial use, Royal Hours shouldn't take up more than two hours.