It could have been a March start, if you were upgraded from a Tambor / Gar or Gato. If it was a March start, or a June of 1943, either one should have assigned you a mission without problem. I'm not certain of the behavior if it would have assigned it in January.
You don't need another Windows domain to have multiple licensed copies of SH4 on your machine. You make a copy of a fresh install of the game, rename it, and then mod that. It ~has~ to be a fresh install to begin with, that has not been played. You could use Rockin Robbins
SH 4 Corruption Management System to help with the chore, or do similar yourself with an archive manager such as 7zip. You would then use MultiSH4 from inside your new copy, and create a new Save game folder. For Fall of the Rising Sun Ultimate, I used FRU, since I already have a regular Fall of the Rising Sun install that is FRS. I used GFO for Game Fixes Only, TMO for Trigger Maru, Overhauled, etc... That is what keeps your separate installs segregated and free of corruption...