LP setup issue

New LP R9 custom shop

Strings buzzing on anything but gentle play on 5th, 6th, and sometimes even 4th string.

I've set the neck at different reliefs ranging from .005 (lowest it will go without torquing the rod harder than I think I should) to .023 (where the nut is sloppy-loose on the rod). The buzzing is slightly better at .023... maybe if I could go to .035 relief I might be OK, and could use it to shoot arrows too.

#6 string height has been set variously up to 6/64s - any more looks/feels odd to me - and nut looks typical.

Is it likely that this can be made right? How?

Thanks in advance for any advice.