I've been bleeding this thing at the banjo's and the screws and tying the brake lever at night with a bungee.  I removed the master cylinder from handlebar to try to release any trapped air.   A short test and the bike stops just fine but the travel is still nearly reaching, if not touching, the grip.  (You know what just occurred to me as I typed this is that I installed larger grips on it the day I brought it home from the dealer.  There's probably an additional quarter inch on the radius of the grip.)  Today I try mass bombing.  I'm going to run a full pint of brake fluid through the system bleeding only at the screws and then tie it off overnight.  Whatever I get, I get.  I'll let you know.

Sounds like you might have  normal travel with old rubber brake lines.  Install 'life-time' stainless hoses from Murph and you will have a rock solid  feel more than stock hoses ever did.
This is  replacement info from the Kawasaki  Service Manual. How old are yours?

Brake hose - replace
Replace every 4 years

Master cylinder. Cup & dust seal
Replace every 2 years

Caliper piston seal & dust seal
Replace every 2 years

I just put my front end back together, disassembled and cleaned my 4 pot Tokico calipers and attached the 2 s/s lines from Murf and bled the system.  I bled till I couldn't seem to get any more air out and yet the brake lever would still make it to the grip and felt spongy.

I zip tied the lever very tight against the grip yesterday and left it on for around 24 hours.  Today I cut the zip tie off and now the lever feels solid at about half way to the grip.

I'm curious. How did zip tying the lever fix your problem?

My guess would be that it puts the master cylinder in a position that allows trapped air in the system to bleed up the lines and through the master cylinder to the reservoir.