You can't earn allied seals from defeating monsters that has no red mandragora icon on top of their names so merits of hunting them without its bill (mandragora icon indicates that the monster is in your currently accepted mark bill, check from Key Item.) and there are no other hunt log aside from the class hunting log.

The elite mark you mentioned are the A and S marks, which you can yield allied seal by just participate in taking it down (with or without party) and unlike the weekly B mark and daily monster/FATE boss, you don't need posted bills to acquire allied seals from them at all so try to find a party to fight these so you can earn the maximum seals easily.