I'm not quite understanding what you're saying, can't picture it. Is this a fix for the 20ml syringes with the thinner rubber plunger cap.
different brand syringes have different plungers. if you have one with the bigger hole use a short piece of 1/4" plastic tubing (you will have to check the size i dont rember what i got) then fit a small ring of this tube inside the larger hole in the plunger will seal it to the carto.
if you hold it so the holes in the carto are at the top (above the juice) while filling it wont force juice into the carto.
i make these with 10 and 20 ml they work great.
you can fill it with any kind of syringe you can get in there - pointed right through the cap or blunt down the edge
or add a fill screw because its just a diy version of a Gummy tank - feel free to look it up lol
oh if you take it from nice cool ac into hot outside it will usually start gurgling lol