While it is a good idea to let the engine sit for a while so the oil can run down, you still want the oil hot. Not goto hospital cause u got 3rd degree burns hot, but hot. This makes sure any shit in ur oiling system is still suspended in the oil and will come out when you drain it instead of settling on the bottom.
And i havent worked on a skyline personally, but can you drain all the oil from the sump with the front jacked, most cars u really should put the rear on stands aswell.