That's okay if you can't recall the P/O pressure. You can do more tests when the Mikuni parts come in and you install them. Remember to do 3 pop off tests to get an average pressure for each carb.
I would just use the new needle/seats that are coming in the kits.
The tip with the rubber on it is the Viton tip(needle). The tip is coated for sealing purposes. That needle lifts up when the P/O pressure has been exceeded under the Valve where the needle sits in and allows fuel to flow. The spring is the "gate keeper" as it only allows fuel to flow as the fuel pressure builds under the valve. Once the P/O pressure exceeds the spring tension. That's when the fuel starts to flow. That is why Valve size(1.5 for yours), P/O, jets(142.5 Main & 70 Pilot), spring(in grams) and the carbs' passage ways like the Bypass holes all need to be squeaky clean and functioning properly so that the motor can draw fuel to feed the engine.
These machines can be a pain and will sometimes make you pull your hair out!
But you're a pro mechanic and have the skill set to work this out. You might feel a little unfamiliar at times. But folks on here have a lot of knowledge and know how from first hand experience working on them and will guide you to getting this ski going!
...and you've already said it. Everything will be ready for next season to ride the crap out of this ski and to have lots of fun and great memories as your smiling ear to ear with the wind and water in your hair!
But also recall this was a "project" ski. You know that projects take time to work on and to get up to speed.
So hang in there!