Moridin or a Moridin/SH combo is in no way obvious at the end of TFoH. Both characters and transmigration weren't really introduced to us until after Asmo's death.

There is also no indication that Bashere is under Moridin's Compulsion, if you read his PoV.

If (TP) balefire was used to kill Asmo, that would already be reason enough why he wasn't transmigrated. Nothing indicates that standing in a Gateway, which leads to a place at SG, would hinder the DO to transmigrate you.