Will a shift star kit solve my downshift issues on my FZ6R?

My fz6r when shifting down to lower gears doesn't like to shift down. you have to keep pressing it many times for it to get down. Seems to be an issue with most of them. It shares the same bottom end with the 03-5 r6. It's not a huge issue but gets extremely annoying after awhile and gets worse the longer it's been running.
Question is will a shift star kit help with the positive down shifting or is this something I' just gonna have to deal with?

Exact same issue on mine.

Also shifting up (usually from 1st to 2nd), the gear will engage but the shifter frequently gets stuck in no man's land until you pull in the clutch or blip the throttle a bit.

Hoping for something that can improve the shifting on this bike.

shift stars lobes on aftermarket shift stars Ive installed were all reshaped both in up and down direction, so both up and down would be affected by the new stars lobe geometry

Will that fix your shifting I cant say, but they usually also come with a stronger detent spring and depending on the bike a new roller arm also that actually has a real bearing in it instead of a riveted on metal roller.

After replacing second gear on my CBR, I installed a Factory Pro shift kit. If I got lazy shifting, the stiffer spring and different profile shift star would ALWYAS finish the shift. For me, it was well worth the cost. I have not mis-shifted since. (on that bike )