What you show in the picture is the way it should be.
One thing, though. Look at both the "hooks" on the shift claw in your picture. One is farther away from the pin than the other. There is more gap at the rear claw than at the front. This makes for some possibility of missed shifts for one shift lever direction.
Kawasaki has a shift stop pin that has an eccentric that will adjust the claw front to rear, and allow centering of the claw on the pins. You should get one of those pins, or, modify the stock non-adjustable one to center it.
The eccentric actually sets the spring on the lever, to move the claw. When all is right, there should be no slop in the lever against the spring, nor from the eccentric to the spring. careful adjustment of the pin stems will get this done.
If the claw is adjusted way out f specification, then the claw may not click itself back into the correct position to pull the next pin on the drum, missing a shift.
Real H1R and H2R's had a claw like some of the dirt bikes have, with the lower claw and an upper one. The upper claw was there to stop the drum and not overshift the drum into a false neutral between gears, and/or into a higher gear. On those, when the shifter has moved the claws, the claws stop the pins in two places not allowing further movement of the drum, until the claws are moved back into the central position for the next shift.
I've got a claw for a dirt bike here someplace, might try to send someone a pic of it to post, just for info for everybody. These 2 claw claws were never put into the stock street bikes, they only got the single claw levers.
Sorry, it has been years, and I don't have/remember the p/n for the eccentric stop pin, but...Dave C bought one for his pighorn, may still have the p/n. (92043-057)
Shifter stop pin is positioned at the bottom of the shift shaft/claw holder. It is the pin that both the hairpin spring and lever fit around. It is retained in the cases by a thread and jamb nut.
It isn't just the stop pin that dictates the centering
of the shift claw, but the legs of the spring that go past the pin as well. I've
had to bend the legs of the pins to get centering, and trim the spring holder to
keep the legs tight against the pin.
There are eccentric stop pins available, so this can be adjusted, look at mraxl's service bulletins/factory directed modifications section (92043-057). The adjustable pin was used on almost every Kawasaki engine that used this kind of shifter lever after its implementation date.
As far as overshifting, the pin doesn't do much to stop it. Look into the double claw type shift levers of some Kawasaki dirt bikes and I think, the S series bikes. They use a standard lower type pin claw, as is seen in the pics, and another over the drum claw, that positively stops the lever and drum from going too far during its rotation between gears.
When the drum gets to the center of the next gear, two pins contact two pawls on the claws, and no overshift is the result. H1R, H2R and KR750 used this claw setup as well. Worked on both upshift and downshift.
The actual S series shaft and claw will fit directly into the H cases, but...
There is a ledge at the top rear of the case that needs to be trimmed back to clear the upper claw, which is the same cut the H series racer cases had. This ledge is just above the starter shaft stop bolt, and catches oil for the starter gear. The ledge isn't critical, and once cut, will not adversely affect the starter gear oiling.
The S series shaft doesn't extend past the weld at the shaft to claw on the right end, so, the clutch cover would have to be closed off at the shift shaft hole. The shaft only protrudes past the left side of the cases about an inch, just enough to get in the way of the frame at the engine mounts. These two things could be rectified with a simple machine/weld operation, switch the S series shaft for an H series one, weld them together, cut the case, done deal.
I stuck an S series claw into an H2 case set earlier today, but...I don't have a digital camera, so I couldn't take pics, and even if I could, I don't know how to post them. If I get time tomorrow, I'll do some measuring and see if the claw bar length is right, etc.