Biblical oil? I think frankincense and myrhh were largely burnt - still the only way to get at the Boswellic acids in the frankincense. As an aside I would suggest given the tendancy then as now in that part of the world to stone anyone who operated incorrectly we can take it that frankincense and myrrh were generally regarded as safe.
That said personally I think there was some very limited essential oil available in biblical times but it was pretty restricted to animal uses and the religious and perfume uses already described.
Still lets do some detective work on juniper. Sheep were kept and sheep need to be sheared. In a hot climate cuts from the shearing would go septic and your flock would not multiply. I dont buy that there was no water available for crude hydrodistillation. Theres plenty of water in the Sea, River Jordan and Nile and of course sheep need water.
Copper pots would have been available but not retorts as we know them with a very restricted opening to the condensor. make it too restricted and how do you get a significent quantity of plant material in? etc. Yes the great problem with producing aromatic oils is how do you condense them? You can heat up plant material, wood chips particularly, but the steam from the pot just flies off with the aromatics without condensing.
However a sheep's fleece makes a pretty efficient condensor so could go over the top of the cooking pot. Care though with that fire! That implies a fairly big pot and sophisticated operation. More sophisticated production would have been possible by putting a pot with the plant material inside a bigger pot with an outer layer of water being heated up. So the result of all this detective work? My guess and its only a speculation is that there could have been some limited production of juniper oil as an antiseptic besides cedarwood oil. Theres a need for it and all the tools are to hand and it would have made a useful trade good. I would imagine juniper oil would have been the oil of choice.
While the woody oils might have been candidates for distillation their use in food and drink as flavouring is very limited so there would have been no great inventive to distill essential oils important those the anti-insect and anti-septic effects of these oils may have been.