Good find on the needles on MedVet. I have bought plenty of syringes from them but never looked for needles, although I have only purchased the non-sharp type dispensing tips to date. And, I really don't want sharps laying around.
As for your idea of needles through a cork, you could do that. As you can see, mine works by attaching the needles to the syringe and the tubing leads to the kettle with the needles acting as an adapter for the tubing . The tubes are held to the kettle with a clothespin. The syringe pump sits on a stand (aka brick) next to the water bath (aka temperature controlled crock pot). So, in a sense, my pump is not really injecting with much pressure at all.
What you want to happen is that the liquid is injected subsurface and that you get all of the chemical out of the syringe and the line since AgNO3 is not cheap. If you are trying double jet, you want the reactants injected next to each other and I have seen some diagrams that even show an outer shield around the tubes or needles to allow the reactants to mix in a sheltered area.
Another thing I have found is that AgNO3 is building up in the stainless needle on the silver side. Actually it almost looks like metallic silver. I don't know if this is a conditioning effect or I should clean it out.
Mine is set up for double-jet, obviously, but I may "step back" to SRADs for a bit. DJ emulsions have shown to be kind of touchy in terms of finishing. I am guessing that in being more monodisperse, when things go wrong in terms of fog, it goes bad very fast, where a polydisperse emulsion gives a little more room for error. That's why I haven't mentioned anything about making DJ emulsions - I haven't made a good one yet without a lot of fog, although they do work. And no, so far, they aren't higher speed but they have been somewhat higher contrast.
I am thinking about a smaller than 18 gauge needle and tubing in order to get a higher pressure jet but I don't think it will make a night and day difference to the results. Maybe your design idea is what I am really looking for. But, how do you attach the tubing to the needle?