There's also a good chance that the ShB post MSQ gives gear like ARR, HW and SB (haven't done SB in a while) to help players get through earlier content.
The run doesn't start till after the first cutscene.
What I did was create a character, hit the login queue then cancel out of it. The character's now usable for when you need it.
Even archiving the older runs which used the "work around" to a seperate tab so there still viewable.
If it's not a problem for the 20+ hour ARR MSQ run then its fine for the parts the NG+ has been split into. Want rid of the queue timers? Then as above play Healer/Tank for the shorter wait times.
Queue time and dungeon complete should always be included, there included for the MSQ runs so it should be no different with NG+
The MSQ runs can be done in either A single session "SS" or across multiple days as a multi session "MS". A run can use in game time "IGT" or real time through the use of Livesplit ect.
Tried the RDM bug but couldn't get it to work once in any of the lower dungeons I had tried.
Full-game leaderboard->MSQ Tab then there's options for ARR, HW and SB along with the current run rule set
Going by the rules it looks like it has to be HW + patches so 3.0-3.56.