The last log updates should be added after the conversation with Loic ("We met the priest Loic at the end of the trials, but our healthy condition seemed to trouble him.") and then, if you do not block his escape or attack him first ("Loic returned with guards and attacked us, but we defeated them.").
I don't think there is any way to get the quest marked as complete if Loic is dead, but that should not cause any problem with progressing in the game (you can kill him as soon as you meet in Silverglen, if you wish). He should drop a key for the door at the end of the trials, which you must have gotten to activate the portal, as well as a key for the hatch in the church (and the NPCs that were there should be gone now). It is also possible to lockpick the hatch.