Remote PowerShell, WinRM Failures: WinRM cannot complete the operation
Finally solved it, helped by the evidence I recently added to the question:
netsh http show iplist
IP addresses present in the IP listen list:
-------------------------------------------
127.0.0.1
On systems where this was working, that list was empty. This seemed rather counter-intuitive to me at first. Nevertheless, I gave this a go:
> netsh http delete iplisten ipaddress=127.0.0.1
Immediately after, I notice this output from netstat:
>netstat -anp tcp
Active Connections
Proto Local Address Foreign Address State
TCP 0.0.0.0:135 0.0.0.0:0 LISTENING
TCP 0.0.0.0:445 0.0.0.0:0 LISTENING
TCP 0.0.0.0:3389 0.0.0.0:0 LISTENING
TCP 0.0.0.0:5985 0.0.0.0:0 LISTENING
TCP 0.0.0.0:47001 0.0.0.0:0 LISTENING
TCP 0.0.0.0:49152 0.0.0.0:0 LISTENING
TCP 0.0.0.0:49153 0.0.0.0:0 LISTENING
TCP 0.0.0.0:49154 0.0.0.0:0 LISTENING
TCP 0.0.0.0:49155 0.0.0.0:0 LISTENING
TCP 0.0.0.0:49175 0.0.0.0:0 LISTENING
TCP 0.0.0.0:49179 0.0.0.0:0 LISTENING
TCP 0.0.0.0:49190 0.0.0.0:0 LISTENING
TCP 10.115.63.107:139 0.0.0.0:0 LISTENING
TCP 10.115.63.107:3389 10.115.13.25:64873 ESTABLISHED
TCP 10.115.63.107:49235 192.168.40.146:445 ESTABLISHED
TCP 10.115.63.107:49291 192.168.40.45:8014 ESTABLISHED
TCP 169.254.34.30:139 0.0.0.0:0 LISTENING
And indeed, WinRM works like it should.
I surmise, via testing, that if no HTTP listener is configured, then all HTTP listeners will bind to the default entity: 0.0.0.0. Because a loopback address was configured as a listener address, the listener was binding to this address instead.
At some point, I must have taken some action that caused this configuration, though I'm not sure how. At any rate, it's working fine now. Thanks all.