A progress report:
Using Benny's Wake-on-LAN application above at "Here" (with extensive use Benny reports high reliability) for starting my RU host machines:
I've thus far over the Internet (with computers NOT on the same subnet) started one remote host from S5 and performed RU Viewer shutdown (to S5), and successfully repeated the start and shutdown cycle; and performed the same process with another computer pair starting from S4 and hibernating to S4.
Getting WOL working is mainly a matter obtaining a DDNS provider; and making correct settings in you router, BIOS, Ethernet network adapter (NIC), firewall, anti-malware software, and disabling "Fast Startup" under Windows Power & Sleep. Not all will always be required.
With the ability to start from S4 and hibernate to S4 on my production machine I have what I need. I'm still experimenting with starting from (the slightly preferable) S5 state on that machine but suspect that I might be up against a hardware limitation.
More to come.