- I moved the Sapphire RX 460 2GB into my main AM3+ machine for one night, and had no problems for several hours of heavy gaming.
- I upgraded my aging Socket AM2 rig to a new FM2+ rig, and the RX 460 has not had any problems since, with plenty of gaming. (1+ month)
Based on the posts I have been seeing, there is something wrong with the RX 460 PCI-e power or bandwidth on computers with older PCI Express revisions. It's unfortunate because the RX 460 seemed to be shaping up to be "A good upgrade for older machines" especially since it doesn't need external power.
As it stands, I guess until these issues are resolved, I wouldn't use RX 460 in an old rig. It looks like someone fixed it mostly by underclocking / undervolting in WattMan. Probably best to do that as a workaround to the problem.
Closing this out as being fixed: don't use RX 460 in older systems.