The stock tapered Timken wheel bearings need very little(.003 to .008 or so), if any, end play. Think of the same type and brand bearings in the third member
They have a ton of preload on them and live for ever. My message is to reduce the end play one way or the other
As already mentioned the original clutch typ posi and the later cup and cone posi in the 8 3/4 used a set of floating pins or a floating block to set the axle end play
How is the left side end play, the axle with no adjuster on it? Both sides need to be checked for total end play. Have you tried adjusting the end play with the stock adjuster yet? If not now is the time to try it
Scerw it in to reduce the end play
Don't we love after market parts
BTW, the Green axle bearing kits that Dr Diff sells work good on the street, that may be your only viable option if you can't make the end play adjust like you want it
I use them on my cars with spools in them on the street