Check all the mating surfaces width, the groove on the barrel, the pin and tangs on the forks, the groove the fork rides in. all the clearances are cumulative. Also roll the slide shafts on a glass plate and check the gears for rocking on the shafts, any combination of these together can cause the issues your seeing for the neutral trouble.
Were the forks replaced with the backcut, they usally need to be if theres any jumping out of gear . They get tweaked by a few thousandths and it's not noticable unless installed and moved just rite.