I have also twiddled around some "XHCI mode" options in the BIOS, which may have fixed the issue - a different USB3 enclosure stopped emitting periodic resets once I turned some inscrutable nonsense from "Auto" to "Enabled". Was that the problem? Will I ever know? I guess I'll have to try again with an external volume stress test, since the internal SATA connections are (thus far, at least) 100% error-free under an hours-long stress test.