The DO reincarnated Ishy (I think probably around 7 months) and Cyndane (I think probably around 3 months) much faster than the *gars (who were reincarnated after 5 other Forsaken died). This could indicate that the more powerful the DO becomes, the faster he can transmigrate.

RJ stated, though, regarding transmigration that "the body has to be basically healthy and sound, and neither too young nor too old. After all, the Dark One wants his servants to be effective, and a body that meets those basic requirements is more desirable than one that doesn't. Since there is no stockpile of such bodies, the only way for someone to die and immediately be reincarnated would be a matter of pure chance. That is, the death occurred when a suitable body was on hand for some other reason. "

This last sentence even strongly implies that it's of course theoretically possible that the DO reincarnates someone immediately.

Obviously it also isn't such a big problem to get a suitable body. RJ didn't say that the previous owner of the body has to be a channeler. It also doesn't seem likely considering that the saidin-channeler Balthamel was put into a female body. Besides that, the Shadow would even have access to channelers, especially in the BT and the WT.

RJ said that the DO is under a certain constraint in the 3rd Age, because he doesn't have that many good channelers in his view. "The Dark One [...] believes that his people from the Age of Legends are in all practical ways better - for which read better trained, more capable, and thus better able to serve him efficiently and effectively - than the people of the present time." Therefore the DO "tries to conserve his resources, using and reusing those he might have killed himself, or ordered killed, in a time where there were thousands to equal them."

This shows that the DO would normally want to transmigrate Osan'gar, who didn't even betray him.

Also Aran'gar mentions in KoD, ch.3:
"Something had been done to punish Mesaana's failure to appear at Shadar Logoth. but what? Once, dereliction on that scale would have meant death. They were too few for that, now."

This stresses the DO's constraint.

Finally - additional to the other chairs at the Garden Party - another comment by Aran'gar there might even foreshadow Osan'gar's reappearance:
"Osan'gar had missed every meeting since the failure at Shadar Logoth. The true question was, was he among the dead or was lie moving in secret, perhaps at the Great Lord's direction? Either way, his absences presented delicious opportunities, but the latter presented as many dangers."

This could indicate that Osan'gar is mindtrapped and working for Moridin now.