I remove all 3 seals and drip down the inside of the metal outer wall, while turning it until I see the liquid just come to the edge underneath the ceramice cup (as you are tilting it) This way, once you place it upright, the liquid will be about a mm below the top of the ceramic cup, so you can pop the 3rd silicone seal back onto the cup (use the flat head of a drywall screw to apply even pressure until the seal snaps back onto the cup. (I forgot who came up with the drywall screw idea but it is perfect)
Now, getting that 3rd seal is tricky until you have done a few. its also easy to damage them a bit, but they still seem to work. always save these if you are throwing out cartos.
I use a tiny flat head screwdriver mayby with a 1/2 mm wide head. I work the head just on top of the ceramic top working outward from the inside hole, while applying outward and upward pressure against the metal outer wall. work all the way around the cup until it pops off. dont panic if you poke thru the seal. its not the end of the world, but just dont slip the head of the driver down into the atomizer coil. sometimes the cup comes up a little with the seal while applying upward pressure. it slides right back down once you get the seal off. Hope this helps. ( I have yet to buy a syringe with a needle, but I do not think your pencil idea with work unless you can force the juice with some pressure) If you have a way to make pressure with the right syringe plunger, it may work nicely.