I would go for 2 and 3. In the first one there is "almost", and in the last one there is a general situation or lets say a routine, which repeated many times in the past.

I start with translating your sentences, hope they make sense. 1)öğlene kadar raftaki deriler neredeyse tükenmişti The magazines that are on the shelf was nearly finished until midday. 2)öğlene kadar raftaki dergiler tükenivermişti The magazines that are on the shelf had been already/quickly finished* until midday. 3)öğlene kadar raftaki dergiler çabucAk tükenmişti The magazines that are on the shelf had been quickly finished until midday. 4)öğlene kadar raftaki dergiler tükenirdi The magazines that are on the shelf used to run out until midday. So the answer is 2 and 3. *When the verb vermek/to give is added to another verb, it means that the verb happens in a shorter time than expected or average.Examples; Beklemediğim bir anda 'Seni seviyorm' deyiverdi. He said I love you (suddenly/unexpectedly). Yola çocuk koşunca, adam aniden arabayı durduruverdi. As a kid run to the road, the man stopped the car suddenly. Actually in all these examples you can use the simple past tense as well (dedi, durdurdu, tükendi) but this form with -vermek is putting some emphasize on how fast it happened.