The silver part in your photo appears to be 16017 (called the jet needle on the parts diagram I am looking at) and the brass part to the left is 13091 (holder, needle jet) and 92063 (jet main).
On most carbs that I have cleaned the 16017 part has not come out of the carb easily/if at all. On my KLR250 it did come out and looked just like in your photo. As I recall it is directional with a bevel on one end that seems to let the needle slide in more easily when the carb slide returns to the down positioni. You can see the tip of 16017 in the throat of the carb when it is seated all the way.
I would recommend not going with stock jetting but understand your frustration with spending the time trying to get the jetting right. From what I read (and found on my one klr250) the stock jetting is pretty lean. With an aftermarket pipe I would think the lean condition would be exagerated on your bike. It should get great milage with the stock jetting though - so there is a benefit!
I have a 125 main and 38 pilot factory Kiehin jets in my stock carb. The bike runs well with a slightly modified stock exhaust and no airbox snorkle.
Be sure to clean out all the jets you cannot replace. On my carb it took many tries at spraying and soaking and finally I had to use a small MIG welder tip cleaning wire to clean out the non-removable main air jet and starter jet to get the bike to start easily and idle well.