Mac locking up for no reason

First, before anyone weighs in: yes, I've already reset SMC & NVRAM.

My Mac mini running Mojave (10.14.3). I just had my first lockup on this machine, though the same exact thing was happening on another Mac mini running Mojave, so I'm convinced it's the OS.

The symptom: the mouse starts beachballing, and everything locks up (clock stops, too), and nothing works except the mouse which I can still move around. I have no other option than to hard power down the machine.

Thankfully I took note of the exact second this happened (01:01:05), and when I booted back up, I looked at the system.log file in Console:

Feb  3 01:01:04 Spacebox xpcproxy[16340]: libcoreservices: _dirhelper_userdir: 529: bootstrap_look_up returned (ipc/send) invalid destination port
Feb  3 01:01:04 Spacebox iTunesCacheExtension[16343]: objc[16343]: Class ITNSImage is implemented in both /System/Library/Frameworks/iTunesLibrary.framework/Versions/A/iTunesLibrary (0x7fffa235b628) and /Applications/iTunes.app/Contents/PlugIns/iTunesCacheExtension.appex/Contents/MacOS/iTunesCacheExtension (0x1086f34b0). One of the two will be used. Which one is undefined.
Feb  3 01:01:04 Spacebox com.apple.xpc.launchd[1] (com.apple.imfoundation.IMRemoteURLConnectionAgent): Unknown key for integer: _DirtyJetsamMemoryLimit
Feb  3 01:01:04 --- last message repeated 1 time ---
Feb  3 01:01:04 Spacebox com.apple.xpc.launchd[1] (com.apple.xpc.launchd.domain.pid.IDECacheDeleteAppExtension.16341): Path not allowed in target domain: type = pid, path = /Applications/Xcode.app/Contents/Frameworks/IDEKit.framework/Versions/A/XPCServices/IDETouchBarSimulatorService.xpc error = 147: The specified service did not ship in the requestor's bundle, origin = /Applications/Xcode.app/Contents/PlugIns/IDECacheDeleteAppExtension.appex
Feb  3 01:01:04 Spacebox com.apple.xpc.launchd[1] (com.apple.xpc.launchd.domain.pid.IDECacheDeleteAppExtension.16341): Path not allowed in target domain: type = pid, path = /Applications/Xcode.app/Contents/SharedFrameworks/LLDB.framework/Versions/A/XPCServices/RootDebuggingXPCService.xpc error = 147: The specified service did not ship in the requestor's bundle, origin = /Applications/Xcode.app/Contents/PlugIns/IDECacheDeleteAppExtension.appex
Feb  3 01:01:13 Spacebox com.apple.xpc.launchd[1] (com.apple.DumpGPURestart): Service only ran for 1 seconds. Pushing respawn out by 9 seconds.
Feb  3 01:01:27 Spacebox com.apple.xpc.launchd[1] (com.apple.DumpGPURestart): Service only ran for 5 seconds. Pushing respawn out by 5 seconds.

I don't know if there's anything useful there. Anyone know how else I can troubleshoot this?