You are doing good! I haven't got quite that far yet...
Today's clue: The guild that committed the theft at 1:00 a.m. did not use a disguise.
So that means we have now all the times!
So here's what I've got so far, I'm sure there's more to it also...
Clue: The Oasis Runners stole an item sometime before the guild who bribed a guard.
Clue: Of the guild that bribed a guard and the Pyramid Prowlers, one stole Pocket Chess and the other committed the theft at midnight.
--> OR didn't bribe a guard, steal the Pocket Chess or commit theft at midnight.
--> Because midnight is the earliest time, and the guild that bribed the guard couldn't have stolen the item at midnight.
So PP committed the theft at midnight and the guild who bribed a guard stole Pocket Chess.
--> Because 5 am is the latest time, OS didn't commit the theft at 5 am.
Clue: Pocket Chess was not stolen by the Sun Chasers, nor was it stolen at 2:00 a.m.
--> SC did not bribe the guard because Pocket Chess was stolen by guild who bribed a guard.
Clue: The guild that climbed the palace walls committed the theft sometime after the Wedding Ring was stolen.
--> Wedding Ring was not stolen 5 am.
--> Guild that climbed the palace wall didn't commit the theft at midnight. So PP didn't climb the palace wall, because PP committed the theft at midnight.
Clue: The guild that used invisibility committed the theft one hour before the Dagger Clan.
--> The guild that used invisibility committed the theft didn't do it 5 am.
--> Also DC didn't commit the crime at 5 am, since there are 2 hours between 5 am and 3 am.
Clue: The Illuminated Menuscript was either stolen using invisibility or by bribing a guard.
--> Pocket Chess was stolen by bribing a guard, so Illuminated Menuscrip was stolen using invisibility.
Clue: The guild that used invisibility committed the theft one hour before the Dagger Clan.
--> Illuminated Menuscript was not stolen 5 am or by DC.
I hope I got this right... I'm sure there is more, I'll keep digging...