Won't go into 2nd on the ground

Last time I had the 440 out (3rd ride of spring) on my way home I could not get it to shift into 2nd. I had been having difficulty with it going into 2nd and falling out of 2nd into neutral but it was very intermittent. This time I ended up getting home (about 7 blocks) before any success. I noticed the neutral indicator, at the same time, was off and not always being accurate. When I got it parked I put it on the center stand and it shifted without any problems that way but still not when bearing a load. From reading around it sounds most likely a bad shift fork but I wanted to get your guys opinions. If it is a shift fork is it easy enough to fix myself or worth paying the shop to do and have it ride ready sooner than later?

Most KZs work exactly opposite to what you describe. Usually they won't shift into 2nd unless moving. When parked they'll only go into 1st and neutral. This is one of the side effects of the "positive neutral finder" feature.

Sorry, I'll give a little more detail, the bike was running on the center stand when I was testing it.

Running doesn't matter. But rolling does. It shouldn't shift into 2nd if running parked at a light either. Hopefully someone who knows more about the transmission and shifting mechanism will chime in soon.

On the center stand the rear wheel is off the ground so I was able to "roll" it through the gears but it wouldn't when trying to actually ride it.

Have you tried doing a basic clutch adjustment as per the owner's manual?